Factors of 157
2026-02-28 11:16 Diff
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Last updated on December 11, 2025

In this topic, let's learn about factors. It is scarce to find numbers that will divide a given number up to the smallest unit without remainder. These numbers are known as the factors, and learning about factors happens when a student comes across a number or number pair in the real world.

What are the factors of 157?

How to find the factors of 157

There are many methods which the students can use to find out the factors of a number. Below you can find some of these methods.

  • Multiplication method
  • Division method
  • Factor tree

Finding factors using multiplication method

Multiplication method is quite an easy method where we find the pair of numbers which when multiplied with each other give the desired number. For 157 the pairs are.


1 × 157 = 157


Hence, we can conclude that the factors of 157 are 1 and 157.

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Finding factors by division method

In the division method, you need to divide the given number 157 by every number starting from 1. If any number is able to divide it without leaving any reminder, then that number is considered as one of its factors.


157 ÷ 1 = 157 (no remainder)


157 ÷ 157 = 1 (no remainder)
 

Prime factors and prime factorization

Prime factorization is done by dividing the number by prime numbers to see which prime number is able to divide it, and if it does, then that number is considered as a prime number.


157÷1= 157 (1 is a prime factor).


157 is also a prime number. Therefore, prime factors of 157 are 1 and 157.

Factor tree

A factor tree is a form of number tree, which is a diagram which represents simple division, where the number at the top is divided until it reaches a prime number or cannot be further divided.
  

Common mistakes and how to avoid them in factors of 157.

It is quite normal for students to commit a few mistakes while trying to find out the factors of a number. Below are a few such mistakes and how to avoid them.

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Problem 1

Is 20 a perfect square number?

Okay, lets begin

No, 20 is not a perfect square.
 

Explanation

√20 ≈ 4.47


4.47 is not an integer.
 

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Problem 2

What is the sum of all the factors of 48?

Okay, lets begin

1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 168
 

Explanation

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48


Sum of factors: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 120
 

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Problem 3

If a number has exactly 4 factors, what could it be?

Okay, lets begin

 16
 

Explanation

9 = 32 so its factors are 1, 3, and 9 (3 factors)
16 = 24 so its factors are 1, 2, 4, 8, and 16 (5 factors)
 

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FAQs on factors of 157

1. How many odd factors does 15 have?

By applying the division method on 15 we find out that its factors are 1, 3, 5, and 15. Out of these factors, none of them are even, hence 15 has no even factors.
 

2.Why can't 0 be a factor of any number?

Zero cannot be a factor of any number because of the fundamental property of factors, a factor is a number that when divides another number, the results will have no remainder or remainder dropped.

3.Is 157 a composite number?

A number that can only be split by two distinct divisors is a prime number, 157 has only two divisors, so it’s a prime number and not a composite number.
 

4.What are the factor pairs of 21?

When we apply the division method on 21 we get to know that 21 has two factor pairs which are (1, 21) and (3, 7). The pairs can be multiplied to get 21 as the product.

5.What is the largest factor of 157?

So for the number 157 the largest factor which is able to divide it, and leaves no remainder is 157 itself, therefore the largest factor of the number 157 is the number 157 itself.
 

Important glossaries for factors of 157

  • Divisor: Any integer that can be divided, with no remainder, by some other integer, is a divisor.
  • Prime Factorization: Writing a number as the product of its own prime factors.
  • Factor Pair: Multiplication of two factors to get a product.
     

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