Factors of 153
2026-02-28 13:16 Diff
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Last updated on December 11, 2025

Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 153. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 153.

What are the Factors of 153?

The factors of 153 or the numbers which divide 153 exactly are:


1,3,9,17,51, and 153.

  • Negative factors of 153: -1,-3,-9,-17,-51,-153.
  • Prime factors of 153: 3,17
  • Prime factorization of 153: 32×17
  • The sum of factors of 153: 1+3+9+17+51+153= 234
     

How to Find the Factors of 153

For finding factors of 153, we will be learning these below-mentioned methods:

  • Multiplication Method
  • Division Method
  • Prime Factor and Prime Factorization
  • Factor Tree
     

Finding Factors using Multiplication Methods

This particular method often finds the pair of factors which, on multiplication together, produces 153.

Let us find the pairs which, on multiplication, yields 153.


1×153=153


3×51=153


9×17=153

So, factors of 153 are: 1,3,9,17,51, and 153.
 

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Finding Factors using Division Method

The division method finds the factors that evenly divides the given number 153. In this process, we have to divide 153 by all possible natural numbers less than 153 and check.


1,3,9,17,51, and 153 are the only factors that the number 153 has. So to verify the factors of 153 using the division method, we just need to divide 153 by each factor.


153/1 =153


153/3=51


153/9=17


153/17=9


153/51=3


153/153=1

Prime Factors and Prime Factorization

Prime Factorization is the easiest process to find prime factors. It decomposes 153 into a product of its prime integers.


Prime Factors of 153: 3,17.


Prime Factorization of 153: 32×17

Factor tree

The number 153 is written on top and two branches are extended.


Fill in those branches with a factor pair of the number above, i.e., 153.


Continue this process until each branch ends with a prime factor (number).


The first two branches of the factor tree of 153 are 9 and 17. Similarly, for 9, we end up having two branches, each with prime factor 3.

Factor Pairs

  • Positive pair factors:   (1,153), (3,51), (9,17)
  • Negative pair factors:  (-1,-153), (-3,-51), (-9,-17).

Common Mistakes and How to Avoid Them in Factors of 153

Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them.
 

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Problem 1

A man has 153 shirts and 51 ties. He wants to divide them equally among some poor people. What is the maximum number of people he can distribute?

Okay, lets begin

Number of shirts: 153


Number of ties: 51


Factors of 153: 1,3,9,17,51,153


Factors of 51: 1,3,17


Common factors of 51 and 153: 1,3,17


Greatest common factor of 51 and 153: 17


So, there will be 17 people for distribution.


Answer: 17 people
 

Explanation

To divide equally, the maximum number of people can be found through the Greatest Common Factor. Here, we found the GCF, which is the answer.

Well explained 👍

Problem 2

Two airplanes leave the airport at the same time. One leaves every 17 hours and the other every 51 hours. When will they leave together again?

Okay, lets begin

 Time-lapse of the 1st airplane: 17 hours


Time-lapse of the 2nd airplane: 51 hours


Prime factorization of 17:17×1


Prime factorization of 51: 3×17


LCM of 17 and 51: 17×3 = 51.


Both the airplanes will meet each other after 51 hours.


Answer: 51 hours
 

Explanation

To find the time again when two airplanes will meet, we have to find the LCM of the two given time-lapses. So, did prime factorization of both 17 and 51. The LCM is the product of the highest power of each factor.

Well explained 👍

Problem 3

Find the GCF of 153 and 51

Okay, lets begin

 Factors of 153: 1,3,9,17,51,153


Factors of 51 : 1,3,17,51


Common factors of 153 and 51: 1, 3,17, 51


So, the Greatest Common Factor of 153 and 51 is 51.


Answer: 51
 

Explanation

We first listed out the factors of 153 and 51 and then found the common factors and then identified the greatest common factor from the common list. 
 

Well explained 👍

Problem 4

Find the smallest number that is divisible by 3,9,17 and 51.

Okay, lets begin

 Prime factorization of 3: 3×1.


Prime factorization of 9: 32


Prime factorization of 17: 17×1


Prime factorization of 51: 3×17

LCM of 3,9,17 and 51: 3×17= 51


Answer: 51 is the smallest number which is divisible by 3,9,17,51.
 

Explanation

To find the smallest number which is divisible by 3,9,17,51, we need to find the LCM of these numbers.
 

Well explained 👍

Problem 5

Find the LCM of 153 and 150

Okay, lets begin

 Prime factorization of 153: 32×17.


Prime factorization of 150: 52×2×3


LCM of 150 and 153: 32×2×52×17 = 7650.


Answer: 7650
 

Explanation

Did prime factorization of both 150 and 153. The LCM is the product of the highest power of each factor.

Well explained 👍

FAQs on Factors of 153

1.What are the multiples of 153?

 Multiples means the product we get by multiplying integers starting from 1, with 153. Let us list the first five multiples of 153: 153,306,459,612,765,...
 

2.Is 153 divisible by 7?

153 is only divisible by 1,3,9,17,51, 153, but not 7, since 153/7 leaves a remainder of 6.
 

3.What is the GCF of 153 and 27?

Factors of 153: 1,3,9,17,51,153


factors of 27: 1,3,9,27.


Common factors : 1,3,9


Greatest common factor: 9
 

4.What are co-prime numbers?

 Two numbers are said to be co-primes, where one is the co-prime of the other, and their GCF is 1.
 

5.What is the LCM of 153 and 145?

Prime factorization of 153= 32×17
Prime factorization of 145= 5×29
LCM of 87 and 145 = 32×5×17×29 = 22185
 

Important Glossaries for Factors of 153

  • Multipliers - Number which multiplies or a number by which another number is multiplied.
  • Dividers - A number that divides.
  • Prime Factorization - It involves factoring the number into its prime factors.
  • Prime factors - These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.
  • Composite numbers - These are numbers having more than two factors.
  • Multiple - It is a product of the given number and any other integer.
     

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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.