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Number System, Know Definition, Formula , Weightage & Examples

Number System is the foundation of Mathematics. In banking exams, one of the most crucial subjects for mathematical ability is the number system. A basic branch of mathematics known as "number system" examines various number types and their characteristics.
authorImagePriyanka Dahima8 Oct, 2025
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Number System

Key Concepts for Number System

In the context of banking quantitative aptitude, the Number System basics refers to a fundamental area of mathematics that deals with different types of numbers and their properties. Understanding the number system is important for solving various quantitative problems encountered in banking exams and financial calculations. Here are the key concepts covered under the Number System in banking quantitative aptitude:
  1. Types of Numbers:
  • Natural Numbers: Positive integers starting from 1 (1, 2, 3, ...).
  • Whole Numbers : Natural numbers including zero (0, 1, 2, 3, ...).
  • Integers: All positive and negative whole numbers, including zero (..., -3, -2, -1, 0, 1, 2, 3, ...).
  • Rational Numbers: Numbers that can be expressed as a fraction of two integers (e.g., 1/2, 3/4).
  • Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π).
  • Real Numbers: All rational and irrational numbers.
  • Prime Numbers: Natural numbers greater than 1 that have only two factors: 1 and the number itself (e.g., 2, 3, 5, 7).
  • Composite Numbers: Natural numbers greater than 1 that are not prime (e.g., 4, 6, 8).
  1. Place Value System:
  • Understanding the value of digits based on their position in a number (units, tens, hundreds, etc.).
  1. Basic Arithmetic Operations:
  • Addition, subtraction, multiplication, and division of numbers.
  • Properties of operations (commutative, associative, distributive).
  1. Factors and Multiples:
  • Finding the factors of a number.
  • Finding the multiples of a number.
  • Understanding concepts like Least Common Multiple (LCM) and Highest Common Factor (HCF).
  1. Divisibility Rules :
  • Rules to determine if a number is divisible by another without performing full division (e.g., divisibility by 2, 3, 5, 10).
  1. Prime Factorization:
  • Expressing a number as a product of its prime factors.
  • Using prime factorization to solve problems related to LCM and HCF.
  1. Estimation and Rounding:
  • Approximating numbers to a certain degree of accuracy.
  • Rounding numbers to the nearest whole number, tenth, hundredth, etc.
  1. Properties of Numbers :
  • Even and odd numbers.
  • Positive and negative numbers.
  • Understanding and applying properties like the distributive property, associative property, and commutative property.
  1. Simplification :
  • Simplifying complex numerical expressions using the BODMAS/BIDMAS rules (Bracket, Order, Division/Multiplication, Addition/Subtraction).

Number System Formula

Here we have discussed the Number System Formulas  Divisibility Rules:
  • By 2: A number is divisible by 2 if its last digit is even.
For eg. The number 2468 divisible by 2 -  A number is divisible by 2 if its last digit is even. Since the last digit of 2468 is 8 (which is even), 2468 is divisible by 2.
  • By 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
For eg. The number 12345 divisible by 3 - A number is divisible by 3 if the sum of its digits is divisible by 3. Sum of the digits of 12345 is 1+2+3+4+5 = 15. Since 15 is divisible by 3, 12345 is also divisible by 3.
  • By 4: The number is divisible by4 if the last two digits of the number are divisible.
For eg. The number 1236 divisible by 4 - A number is divisible by 4 if the last two digits from a number divisible by 4. The last two digits of 1236 are 36. Since 36 is divisible by 4, 1236 is also divisible by 4.
  • By 5: A number is divisible by 5 if its last digit is 0 or 5.
For eg. The number 1010 divisible by 5 - A number is divisible by 5 if its last digit is 0 or 5. Since the last digit of 1010 is 0, 1010 is divisible by 5.
  • By 6: The number is divisible by 6. If the number is divisible by 2 as well as 3.
For eg. The number 672 divisible by 6 - A number is divisible by 6 if it is divisible by both 2 and 3. Since 672 ends in an even number (divisible by 2) and the sum of its digits ( 6+7+2=15) is divisible by 3, 672 is divisible by 6.
  • By 7: The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0.
For eg. The number 798 is divisible by 7 - The unit digit of 798 is 8. If the unit digit is doubled, we get 16 (i.e., 8 x 2 = 16) The remaining part of the given number is 79. Now, take the difference between 79 and 16. 79-16 =63 Here, the difference value obtained is 63, which is a multiple of 7. (i.e., 9 x 7 = 63). Thus, the given number 798 is divisible by 7.
  • By 8: The number is divisible by 8. If the last 3 - digit number is divisible by 8.
For eg. The number 512 divisible by 8 - A number is divisible by 8 if the last three digits form a number divisible by 8. Since 512 is less than 1000, we check 512 directly. Since 512 8=64 .
  • By 9: The number is divisible by 9. If the sum of its digits is divisible by 9.
For eg. The number 729 divisible by 9 - A number is divisible by 9 if the sum of its digits is divisible by 9. Sum of the digits of 729 is 7+2+9=18. Since 18 is divisible by 9, 729 is also divisible by 9.
  • By 10: A number is divisible by 10 if its last digit is 0.
For eg. The number 230 divisible by 10 - A number is divisible by 10 if its last digit is 0. Since the last digit of 230 is 0, 230 is divisible by 10.
  • By 11. The number is divisible by 11 .If the difference between the sum of even place’s digit and odd place’s digit is 0 or multiples of 11.
For eg. The number 1331 divisible by 11 - A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11 (including 0). For 1331, the sum of the digits in odd positions is 1+3=4, and the sum of the digits in even positions is 3+1=4. The difference is 4−4=0, which is a multiple of 11. Thus, 1331 is divisible by 11.
  • By 12. The number is divisible by 12. If the number is divisible by 3 or 4.
For eg. The number 5864 divisible by 12 - Sum of the digits = 5 + 8 + 6 + 4 = 23 (not a multiple of 3) Last two digits = 64 (divisible by 4). The given number 5864 is divisible by 4 but not by 3; hence, it is not divisible by 12.
  • By 13. To check if a number is divisible by 13, multiply its unit place digit by 4, then add the product obtained to the number formed by the rest of the digits of the number. If the result is 0 or a multiple of 13, the result is divisible by 13.
For eg. 1092 is divisible by 13. Here, the unit digit is 2. When it is multiplied by 4, we get 8, and the remaining part of the number is 109. Hence, the sum of 109 and 8 is 117, which is divisible by 13.

Weightage of Number System

The weightage of the Number System in banking exams can vary depending on the specific exam and the exam-conducting body. However, the Number System is a fundamental topic that forms the basis for many quantitative aptitude questions. Here’s an overview of its typical weightage and importance in various banking exams: Importance of Number System in Banking Exams
  1. Foundation for Other Topics:
  • The Number System forms the basis for understanding more complex topics like algebra, arithmetic, and data interpretation.
  • Strong knowledge of the Number System is essential for solving questions in other areas such as simplification, ratio and proportion, percentage, profit and loss, and averages.
  1. Direct Questions:
  • Number System questions are often straightforward and can be quickly solved, making them scoring opportunities.
  • These questions test basic mathematical concepts, divisibility rules, properties of numbers, prime factorization, LCM and HCF, etc.

Number System Solved Questions

 

  1. Is the number 582 divisible by 3?
Solution : Sum of the digits: 5+8+2=15. Since 15 is divisible by 3, 582 is divisible by 3.
  1. Is the number 7600 divisible by 4?
Solution : Last two digits are 00. Since 00 is divisible by 4, 7600 is divisible by 4.
  1. Is the number 1248 divisible by 6?
Solution : The number is even (divisible by 2), and the sum of its digits is 1+2+4+8=15, which is divisible by 3. Hence, 1248 is divisible by 6.
  1. What is a positive number?
Solution : Positive numbers are those numbers that fall on the right-hand side of the number line after 0. These numbers are used for addition. The value in this case increases as it moves right.
  1. What is an integer?
Solution : An integer is a number that can have either positive or negative values. It is a fraction. It is denoted by z.
  1. What is a number line?
Answer : A number line can be expressed as a line upon which digits starting from 0-9 are mapped. 0 is in the middle. Negative numbers are charted on the left of 0 and positive numbers are charted on the right of 0.

Q7. Which one of the following is not correct?

(a) 1 is neither prime nor composite

(b) 0 is neither positive nor negative

(c) If pq is even, then p and q are always even

(d) 2 is an irrational number

(e) All correct

Answer : (a), (b), and (d)

Q8. Consider the following statements.

  1. Of two consecutive integers one is even.
  2. Square of an odd integer is of the form 8n+1.

Which of the above statements is/ are correct?

(a) Only 1

(b) Only 2

(c) Both 1 and 2

(d) Neither 1 nor 2

(e) None of the above

Answer : (c)

Practice Questions

Practice problems on number system with the use of Number system formulas are given below for better understanding:

Q1. Is the number 1045 divisible by 5? Q2. Is the number 247 divisible by 11? Q3. What is the result of small numbers which are 15? Q4. State the difference between 5 greatest digits and small 5 digits. Q5. If y and w are two numbers that belong to 653yq and it can be divided by 80 then what would be the y+q value?

Related Links
Quadratic Equations Number System
Vedic Maths Pie Chart DI
Time and Work Problem on Ages
Flow Chart DI
Arithmetic DI Permutation and Combination

Number System FAQs

Q1. What are even and odd numbers?

Ans. Even numbers are integers that are divisible by 2 (e.g., 2, 4, 6). Odd numbers are integers that are not divisible by 2 (e.g., 1, 3, 5).

Q2. What are rational numbers?

Ans. Rational numbers are numbers that can be expressed as a fraction of two integers (e.g., 1/2, 3.75).

Q3. What are irrational numbers?

Ans. Irrational numbers cannot be expressed as a simple fraction; their decimal form is non-repeating and non-terminating (e.g., √2, π).

Q4. How do you determine if a number is prime?

Ans. A number is prime if it has no positive divisors other than 1 and itself. To determine if a number is prime: Check if it is greater than 1. Test divisibility by all prime numbers up to the square root of the number.
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