CBSE Class 6 Maths Notes Chapter 3 Playing With Numbers

Example: 1, 2, 3, and 6 are the factors of 6.

Example: 1, 2, 3, and 6 are the factors of 6.

Properties of Factors

Below we have summarized properties of factors -

Properties of factors of a number:

• 1 is a factor of every number.
• Every number is a factor of itself.
• Every factor of a number is an exact divisor of that number.
• Every factor is less than or equal to the given number.
• Number of factors of a given number are finite.

Perfect Numbers

A number that equals the total of its appropriate divisors—that is, factors other than itself—is called a perfect number. Example: Factors of 28 are 1, 2, 4, 7, 14 and 28. Here, 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28 Therefore, the sum of factors of 28 is equal to twice the number 28.

Multiples

The numbers we obtain when we multiply a number by any integer are called multiples of that number. Example: Multiples of 3 are 6, 9, 12, 15, 18 etc.

Properties of Multiples

Properties of multiples of a number:

A number is bigger than or equal to every multiple of that number. There are an endless amount of multiples of any given number. All numbers are multiples of one another.

Ones with the One and the Others

Prime Numbers

Prime numbers are any numbers other than 1 whose only factors are 1 and the number itself. Example: 2, 3, 5, 7 etc.

Composite Numbers

Composite numbers are those that consist of more than two elements. Example: 4, 6, 8 etc.

Divisible by 2 or 5 or Both

Now let's learn the divisibility rules for 2 and 5 -

Divisibility Tests

By looking at the integer's digits, a divisibility rule can tell you if it can be divided by a fixed divisor without the need for division. For the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11, we have divisibility rules.

Divisibility Tests for 2

If one’s digit of a number is 0,2,4,6 or 8, then the number is divisible by 2. Example: 12, 34, 56 and 78.

Divisibility Tests for 4

A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4. Example: 1396 is divisible by 4 since its last two digits, i.e., 36 is divisible by 4.

Divisibility Tests for 3

A number is divisible by 3, if the sum of its digits is divisible by 3. Example: Take 27. Sum of its digits = 2+7= 9, which is divisible by 3. Therefore, 27 is divisible by 3.

Divisibility Tests for 5

If the one’s digit of a number is either 5 or 0, then it is divisible by 5. Example: 75, 90, 100 and 125.

Divisibility Tests for 8

A number with 4 or more digits is divisible by 8, if the number formed by its last three digits is divisible by 8. Example: 73512 is divisible by 8 since its last three digits, i.e., 512 is divisible by 8.

Divisibility Tests for 6

If a number is divisible by 2 and 3 both, then it is divisible by 6 also. Example: 120 is divisible by 2 and 3. Therefore, it is divisible by 6 also.

Divisibility Tests for 7

Double the last digit and subtract it from the remaining leading cut number. If result is divisible by 7, then the original number is divisible by 7. Example: 826 is divisible by 7 since, 82 – (6 × 2) = 82 – 12 =70, which is divisible by 7.

Divisibility Tests for 9

A number is divisible by 9 if sum of its digits is divisible by 9. Example: Consider 126. Sum of its digits = 1+2+6 = 9, which is divisible by 9. Therefore, 126 is divisible by 9.

Divisibility Tests for 11

Find difference between sum of digits at odd places (from the right) and sum of digits at even places (from the right) of a number. If the difference is either 0 or divisible by 11, then the number is divisible by 11. Example: 1234321 is divisible by 11 since, (1+3+3+1) – (2+4+2) = 8 – 8 = 0, which is divisible by 11.

Divisibility Tests for 10

If one’s digit of a number is 0, then the number is divisible by 10. Example: 10, 20, 30 and 40.

Common Factors

The factors of 4 are 1, 2 and 4. The factors of 18 are 1, 2, 3, 6, 9 and 18. The numbers 1 and 2 are common factors of both 4 and 18.

Common multiples

Multiples of 3 are 3, 6, 9, 12, 15, 18,…. Multiples of 5 are 5, 10, 15, 20, 25, 30,… Multiples of 6 are 6, 12, 18, 24, 30, 36,… Therefore, common multiples of 3, 5 and 6 are 30, 60,….

The Prime Factor

Prime Factorisation

Prime factorisation is the process of factoring a number expressed as a product of prime numbers. Example: Prime factorisation of 36 is 2×2×3×3.

Benefits of CBSE Class 6 Maths Notes Chapter 3