Factors of 53

Factors of 53 are the whole numbers that can divide the original number, uniformly or in equal parts. It means after division, there is no remainder left or the remainder is zero. For example, 8 is the factor of 24, because 8 divides 24 into 3 equal parts.

24/8 = 3 [Remainder = 0]

A factor of any number is either less than or equal to the original number. Let us find the factors, pair factors and prime factors of 53 in this article with simple methods.

Factors Pair Factors Prime Factors
1 and 53 (1,53) or (53,1) 53 → 53

How to Find the Factors of 53?

In Maths, factors are the real numbers that can divide the actual number, evenly. Since 53 is itself a prime number, therefore, it will have only two factors, 1 and 53.

53 ÷ 1 = 53

53 ÷ 53 = 1

If we divide 53 by any other positive number, then the quotient produced after division will be a fraction or decimal. Thus, the factors of 53 are 1 and 53.

More Factors

Pair Factors of 53

Pair factors are the numbers that are evaluated in a pair. The product of pair factors of 53 will result in the original number. Hence,

1 × 53 = 53

Or

53 × 1 = 53

Therefore, there is only one pair factor, i.e. (1, 53).

Similarly, we can also find the negative pair factors of 53 that will result in the original number.

-1 × -53 = 53

Therefore, the negative pair factor is (-1, -53).

Prime Factorisation of 53

By the prime factorization method, we can easily find the prime factors of any number. These prime factors are the prime numbers. As we already know, 53 is a prime number, therefore, the prime factorization of 53 is not required.

Check:

We can check if 53 is a prime number or not, by dividing it by other prime numbers. First let us list down the prime numbers from 1 to 53.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53

Now if we start dividing 53 by prime numbers, then we get;

53/2 = 26.5

53/3 = 17.67

53/5 = 10.6

53/17 = 3.11

53/31 = 1.7

Continue dividing up to 47, we will see all the resultant quotients are fractions. Therefore, only 53 can divide it by itself.

Hence,

Prime factorisation of 53 = 53

Solved Examples

Q.1: Find the sum of all the factors of ninety-seven.

Solution: The factors of 53 are 1 and 53.

Sum = 1 + 53 = 54

Therefore, 54 is the required sum.

Q.2: What is the greatest common factor of 53, 57 and 59?

Answer: Let us list down the factors of all the numbers.

The factors of 53 are: 1, 53

The factors of 57 are: 1, 3, 19, 57

The factors of 59 are: 1, 59

Hence, we can see, 1 is the only factor that is common to all. So,

GCF (53, 57, 59) = 1

Q.3: Find the square of 53.

Solution: Square of 53 = 532

= 53 x 53

= 2809

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Frequently Asked Questions on Factors of 53

What are the factors of 53?

There are only two factors of 53, they are 1 and 53, itself.

What are the multiples of 53?

The first ten multiples of 53 are 53, 106, 159, 212, 265, 318, 371, 424, 477 and 530.

What is the divisibility of 53?

The numbers by which 53 is divisible, are 1 and 53.

Is 53 a prime or composite number?

53 is a prime number.

What is 53 as a product of prime?

53 itself is a prime number, therefore, it cannot be written as a product of two or more prime numbers.

Is 53 a perfect square?

53 is not a perfect square, because the root of 53 is not a whole number but a fraction.

√53 = 7.28

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