Is 47 a Prime Number?

Is 47 a prime number? How do you know? While dividing 47 chocolates among friends, you will notice they can’t be divided equally unless shared individually. Or you keep all 47 chocolates to yourself. 

A prime number is a number greater than 1 that can only be divided by 1 and itself. This concept forms the basis for many mathematical calculations in various fields, even beyond mathematics. With 47 as an example, this article lets you explore more about prime and composite numbers.

What is a Prime Number?

A prime number is a whole number divisible only by 1 and itself. If we divide a prime number by any other number, there will always be a remainder. In other words, a prime number has only two factors: 1 and the number itself.

For example, 13 is a prime number because it is only divisible by 1 and 13.

Read More - Numbers: Definition, Types, and Properties

What is a Composite Number?

A composite number is a number that has more than two factors. We know that every number is divisible by 1 and the number itself. So, a composite number includes factors as 1 and the number itself, along with at least another number.

For example, 68 is a number that can be factorized as follows:

68 = 2 x 2 x 17

So, 68 is a composite number because it has two factors, 2 and 17, apart from 1 and 68.

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Differences between Prime Numbers and Composite Numbers

The differences between prime and composite numbers are explained in the table below.

Is 47 a Prime Number or a Composite Number?

To determine whether 47 is a prime number or not, we must check whether 47 is divisible by any number other than 1 and 47. 47 is divisible only by 1 and 47, and there are no other factors of 47.

So, we can say, 47 = 1 x 47

It is a prime number since 47 has no factors other than 1 and 47.

The number 47 has only two factors, 1 and 47. We can’t factorize it in any other way. Since factors of 47 are 1 and 47 only, we can say that 47 is not a composite number.

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What Are the Factors of 47?

Since 47 is a prime number, it has only two factors: 1 and 47. In other words, 47 can’t be evenly divided by numbers other than 1 and 47 without leaving a remainder.

We can check if there are any other factors of 47.

47 is not divisible by 2 because it is an odd number.

47 is not divisible by 3 because the sum of its digits (4 + 7 =11) is not divisible by 3.

47 is not divisible by 5 because it doesn’t end with 0 or 5.

47 is also not divisible by other prime numbers like 7,11, 13, 17, 19, 23, 29, 31, 37, 41, and 43. Therefore, the factors for 47 are only 1 and 47.

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Prime Number Formula to Check if 47 is a Prime Number

There is a formula to find the prime numbers greater than 40. It is expressed as follows:

n2 + n + 41, where n are natural numbers 0, 1, 2, 3,…39.

This formula can be used to verify if 47 is a prime number.

For example,

(0)2 + 0 + 0 = 41

(1)2 + 1 + 41 = 43

(2)2 + 2 + 41 = 47

(3)2 + 3 + 41 = 53 

and so on.

According to this formula, 47 is a prime number.

Read More - Multiplication: Definition, Formula, Examples, Rules, Table

Important Points

Here are some important points to be noted:

• Prime numbers are always odd; only 2 is an even prime number.

• If the sum of the digits of a number is divisible by 3, it is not a prime number.

• Multiples of any number other than 1 are not prime numbers.

• If the prime factorization of a number gives more than two prime numbers, then it is a composite number, not a prime number. 

This article explains whether 47 is prime or composite and how understanding numbers builds stronger problem-solving skills. If you're looking for a fun and effective way to support your child’s maths learning, CuriousJr kids online classes make complex topics simple and engaging. Book a demo today and help your child build a strong foundation in maths through interactive learning.