Factors of 137
2026-02-28 23:26 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-137

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Last updated on December 11, 2025

Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 137 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!

What are the factors of 137?

Factors are whole numbers that, when multiplied, the product is equal to 137. 


137 is a prime number, its only factors are 1 and 137. For every factor, there is a corresponding negative factor, for 137, the negative factors -1, -137. 
 

How to find the factors of 137?

There are various methods we apply to find the factors of any number. Few of them are listed here;  multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
 

Finding Factors Using Multiplication

Step 1: Find all pairs of numbers whose product is 137. 


Step 2: All the pairs found represent the factors of 137. 


137 is a prime number. The only pair of numbers whose product is 137 is 1×137=137. 


The factors of 137 are 1 and 137 only. 

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Finding Factors by Division Method

Step 1: Start by dividing 137 with the smallest number, and check the remainders. 


Step 2: 137 is prime, therefore the only divisors it has are 1 and 137. Any number that is further checked for divisibility leaves behind a remainder.


The factors of 137 are 1 and 137 only. 

Prime factors and prime factorization

— 137 is a prime number.


— The prime factorization of 137 is 137. 


— Factors of 137 are 1,137 
 

Factor tree

— In this method, we make branches that extend from the number to express a number as the product of its factors. 


— In case of 137, only one branch will be extended, as there are no other factors of the number
 

Common mistakes and how to avoid them in the factors of 137

We all make mistakes when it comes to finding factors, especially when it comes to numbers like 137. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them. 

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Problem 1

Is 137 divisible by 4?

Okay, lets begin

Use the divisibility rule for 4, which states that a number is divisible by 4 if its last two digits form a number divisible by 4.


The last two digits of 137 are 37.


Since 37 ÷ 4 = 9.25 (not a whole number), 137 is not divisible by 4.
 

Explanation

This problem helps to confirm that 137 does not have 4 as a factor. By using divisibility rules, we can quickly determine if a number has other possible factors without performing long division.

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Problem 2

Verify if any number multiplied by itself results in 137.

Okay, lets begin

Take the square root of 137 to see if it is a perfect square: 137≈11.7


Since 11.7 is not a whole number, no integer multiplied by itself equals 137.
 

Explanation

 If a number is a perfect square, it has an integer as its square root, which would mean it could be factored into two equal whole numbers. Here, 137 is not a perfect square, so it cannot be expressed as a product of any number with itself.
 

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Problem 3

Can 137 be written as the sum of two factors?

Okay, lets begin

Since 137 is prime, its only factors are 1 and 137.


Adding these two factors gives: 1+137=138


Therefore, 137 cannot be written as the sum of two of its factors.
 

Explanation

With prime numbers, this kind of sum isn’t possible because they only have two factors. For non-prime numbers, however, this sum could sometimes match the number itself or another factor.
 

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FAQs on Factors of 137

1.Why is the number 137 special?

The astronomer Arthur Eddington postulated that the reciprocal of 1/137 was the integer 137 precisely and had obtained the using the method of pure deduction. 
 

2.What are the multiples of 137?

The multiples of 137 up to the count of 10 are → 137, 274, 411, 548, 685, 822, 959, 1096, 1233, 1370. 
 

3.What is the magic number 137?

The number 137 is a fine structure constant and is denoted by the Greek symbol ‘alpha’, ‘𝝰’. It is applied in the formulas that deal with light and matter. 
 

4.What three numbers add up to 137?

A combination of numbers whose sum is equal to 137 are 64,23 and 50. To substantiate, 64+23+50= 137. 
What is the number name of 137?
 

5.What is the number name of 137?

The number name of 137 is written as ‘One Hundred thirty-seven’. The unit’s place is taken by seven, the one’s place by thirty and the hundred's place by one hundred.  
 

Important Glossaries for Factors of 137

  • Factors: numbers that divide the given number without leaving a remainder. 
  •  Prime factorization: breaking numbers down into their prime factors.
  •  Prime factors: Prime numbers that multiply together to form a given number.
  • Composite number: Number that has at least more than one divisor other than 1 and the number itself.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.