Factors

# Factors of 137 | Prime Factorization of 137 | Factor Tree of 137

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 137 | Prime Factorization of 137 | Factor Tree of 137

## Factors of 137

Factors of 137 | Factor Pairs of 137 | Prime factors of 137 |

1, 137 | (1,137) | 137 |

Calculate Factors of

**The Factors are**

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## What are the factors of 137

137 is a prime number with 1 and itself as its factors. To think of this another way, we could say that all possible factors for 137 equal just two – one being its own value (1 x 137 =137) and the other factor simply being ‘one’ (1×1=137). A few quick calculations will tell us these two simple answers to our question: what are the factors of 137? The answer is… 1 & 137!

## How to Find Factors of 137

The most popular methods to find the factors of a number are given below and the same can be used to find the factors of 137.

- Factor of 137 using Multiplication Method
- Factors of 137 using Division Method
- Prime Factorization of 137
- Factor tree of 137

## Factors of 137 using Multiplication Method

Factors are numbers that multiply together to form a certain number. To find out which factors belong to 137, we can use the multiplication method. All you have to do is take 1 and it’s a friend (137) and join them up in pairs; then just multiply both of them together until each pair makes 137. That way, you’ll discover that those same two friends —1 & 137—are actually its only set of factors!

## Factors of 137 Using Division Method

Prime numbers are special types of integers that can only be divided by themselves and one. To figure out a prime number’s factors, the easiest way is to use multiplication:

- Take each value from 1 up until the given integer (in this case 137) and multiply it with ‘137’.
- If your answer is equal to ‘137’, you have found two of its factors! In our example here we multiplied 1×137 = 137 so this tells us both these values are in fact factors for 137 – an interesting yet very straightforward perspective on Prime Numbers.

## Prime Factorization of 137

Calculate Prime Factors of

The Prime Factors of 137 =

137

Understanding prime factorization is an important skill for students of Mathematics to master.

- To put it simply, the expression of a number as its product of prime factors – also known as “prime factorization” – allows us to break down any given number into smaller parts made up only of their most basic elements.
- For example, 137 can be broken down into 1 and 137 since it has no other positive integer divisors except itself!

## Factor tree of 137

The factor tree is an ingenious way to learn about prime factors. In this case, 137 can only be broken down into one prime factor – itself. Through exploring the relationships between numbers and their composite parts with a tool like a factor tree, students gain insight into how mathematics works on many different levels.

## Factor Pairs of 137

Calculate Pair Factors of

1 x 137=137

So Pair Factors of 137 are

(1,137)

To understand the factor pairs of 137, it’s important to know that as 137 is a prime number, its divisors are just 1 and itself. Therefore, when looking for its factor pairs you can start by dividing it with each number up until the square root of 137. If there’s an even division result then this means that both numbers in combination would multiply together to equal 137 – thus creating two distinct factoring pairings: (1,137) & (137;1). As long as students remember these key points they will have no problem understanding how to calculate any given figure’s individual factoring pair!

## Factors of 137 – Quick Recap

**Factors of 137:** 1, 137.

**Negative Factors of 137:** -1, -137.

**Prime Factors of 137: **137

**Prime Factorization of 137:** ** **137

## Fun Facts of Factors of 137

137 is an odd and special number!

- It’s the 33rd prime, meaning it can only be divided by 1 and itself with no remainder.
- 137 also belongs to the Mersenne Prime family – a rare kind of prime formed when you take 2 raised to any other expressible prime power (in this case p) minus one.

## Examples of Factor of 137

**1. If Jorge has 137 apples, how many baskets of 9 can he fill?**

**Answer: **Jorge can fill 15 baskets with 9 apples each (137 ÷ 9 = 15).

**2. What is the greatest common factor of 27 and 137?**

**Answer: **The greatest common factor (GCF) of 27 and 137 is 3 (which is 3×3).

**3. William has 34 red marbles and 68 blue marbles. What is the least common multiple of these two numbers?**

**Answer: **The least common multiple (LCM) of 34 and 68 is 136 (34 x 68 = 2312, which can be divided by 2 to get 1160, then divided by 4 to get 290, then divided by 19 to get 36, and finally by 4 again to get 9).

**4. How many combinations of 11 and 13 will equal 137?**

**Answer: **There are only 2 combinations of 11 and 13 that are equal to 137 (11 x 13 = 143; 113 x 1 = 113).

**5. How many pairs of 17 do you need for a total sum of 137?**

**Answer: **You need 8 pairs of 17 for a total sum of 137 (17 x 8 = 136).

**6. If I divide 137 into groups of 11, how many groups will I have left over?**

**Answer: **You will have 3 groups left over if you divide 137 into groups of 11 (137 ÷ 11 = 12 with remainder 5).

**7. What number do you multiply by 18 in order to get a product of 244? **

**Answer: To get** a product of 244 when multiplying by 18, you would need to multiply by 14(244/18=13.6 with remainder2so 14*18=252>244).

**8. If Kyle collects coins that are worth 0.25 each, how much money does he have in 56 quarters? **

**Answer: **Kyle has 14 dollars in 56 quarters (56 x 0.25 = 14).

**9. Find the prime factors for the number 137 using exponential notation for any prime factors that appear more than once in the factor tree. **

**Answer: **The prime factors for 137 using exponential notation are 3²×17 or 3⁰×3²×17.

**10. How many unique factors does 137 have? **

**Answer:** There are 7 unique factors for the number 137 (1, 3, 9, 11, 27, 33, and 137).

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## Frequently Asked Questions on Factors of 137

**What is a factor of 137?**

A factor of 137 is any number that can divide137 without leaving a remainder. The factors of 137 are 1, 3, 9, 11, 27, 33 and 137.

**Is 18 a factor of 137?**

No, 18 is not a factor of 137 because there will be a remainder (137 ÷ 18 = 7 with remainder 13).

**How many factors does 137 have?**

There are 7 factors for the number 137 (1, 3, 9 ,11 ,27 ,33 and 137).

**How can I find the prime factors of 137?**

To find the prime factors of 137, you need to list all its factors and identify which ones are prime numbers (such as 2, 3 or 5). The prime factors of 137 are 3 x 47 or 3 x 11 x 13 .

**What is the greatest common factor of 136 and 137?**

The greatest common factor (GCF) of 136 and 137 is 1.

**Can 135 be divided evenly by 132?**

No, 135 cannot be divided evenly by 132 because there will be a remainder equal to 3 (135 ÷ 132 = 1 with remainder 3).

**What is the least common multiple(LCM)of 136 and 137?**

The least common multiple(LCM)of 136 and137 is 1352 (136×137=1352 ).

**What two numbers can you multiply together to get the product 135?**

You can multiply 45 x3 or 15 x 9 to get the product 135.

**If someone has 56 quarters, how much money do they have in total? **

56 quarters equals 14 dollars ($14; 56*0.25=14 ).

**Is one a factor of every number?**

Yes, one is considered an “identity” factor for every number as multiplying it by one will not change its value.

Written by

Prerit Jain