Factors of 87
2026-02-28 01:12 Diff
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Last updated on December 11, 2025

Factors of any number are the whole numbers that can divide the number completely. Why are factors important to learn? For mathematical approaches, factors are used in organizing and bringing more efficiency to any task. In this article, let's learn how to solve factors of 87 easily.

What are the Factors of 87?

Factors of 87 are those numbers that can divide 87 perfectly. The factors of 87 are:


1,3,29 and 87.

  • Negative factors of 87: -1, -3, -29, -87
  • Prime factors of 87: 3
  • Prime factorization of 87: 3×29
  • The sum of factors of 87: 1+3+29+87= 120

How to Find the Factors of 87

For finding factors of 87, 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 87. Let us find the pairs which, on multiplication, yields 87.


1×87=87


3×29=87


From this, we conclude that, factors of 87 are:1,3,29 and 87.
 

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Finding Factors using Division Method

The division method finds the numbers that evenly divides the given number 87. To find the factors of 87, we have to divide 87 by all possible natural numbers less than 87 and check.


1,3,29,87 are the only factors that the number 87 has. So to verify the factors of 87 using the division method, we just need to divide 87 by each factor.


87/1 =87


87/3 =29


87/29=3


87/87=1

Prime Factors and Prime Factorization

Prime Factorization is the easiest process to find prime factors. It decomposes 87 into a product of its prime integers.


Prime Factors of 87: 3.


Prime Factorization of 87: 3×29 
 

Factor tree

The number 87 is written on top and two branches are extended.


Fill in those branches with a factor pair of the number above, i.e., 87.


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


The first two branches of the factor tree of 87 are 3 and 29.


Factor Pairs:


Positive pair factors:   (1,87), (3,29).


Negative pair factors: (-1,-87), (-3,-29).

Common Mistakes and How to Avoid Them in Factors of 87

Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them.
 

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Problem 1

Find the GCF of 87 and 58

Okay, lets begin

 Factors of 87: 1,3,29,87


Factors of 58: 1,2,29,58


Common factors of 87 and 58: 1,29


So, the Greatest Common Factor of 87 and 58 is 29.


Answer: 29
 

Explanation

We first listed out the factors of 87 and 58 and then found the common factors and then identified the greatest common factor from the common list. 
 

Well explained 👍

Problem 2

Find the smallest number which, when divided by 29 and 87, leaves a remainder 5 in each case.

Okay, lets begin

First finding the LCM of 29,87


Prime factorization of 29 =29×1


Prime factorization of 87 = 29×3


LCM of 29,87 = 29×3=87


The smallest number which, when divided by 29 and 87, leaves a remainder 5 in each case is = LCM + 5 = 87+5 =92


Answer: 92
 

Explanation

 First find the LCM and just add the remainder with that to get the smallest number.
 

Well explained 👍

Problem 3

The area of a rectangle is 87 square units. If the length is 3 units, then what is the measure of its width?

Okay, lets begin

Area of rectangle: 87 sq units


Factors of 87: 1,3,29,87


We know that the area of a rectangle is the product of its length and breadth.


Given, length= 3 units


There exists a factor pair of 87, which is (3,29). Hence, width is 29 units. Let’s check it through the formula for area.


So, length×width = area


⇒ 3 × width = 87


⇒ width = 87/3 = 29


Answer: 29 units
 

Explanation

Used the concept of factor pairs for 87 and rechecked using the formula for finding area of a rectangle.
 

Well explained 👍

Problem 4

Find the smallest number that is divisible by 3,29.

Okay, lets begin

 Prime factorization of 3: 3×1.


Prime factorization of 29: 29×1

LCM of 3,29: 3×29 = 87


Answer: 87 is the smallest number which is divisible by 3 and 29.
 

Explanation

To find the smallest number which is divisible by 3,29, we need to find the LCM of these numbers.
 

Well explained 👍

Problem 5

What is the sum of the factors of 87 and 88?

Okay, lets begin

 Factors of 87: 1,3,29,87


Sum of the factors: 1+3+29+87= 120


Factors of 88: 1,2,4,8,11,22,44,88


Sum of the factors: 1+2+4+8+11+22+44+88 =180
 

Explanation

added all factors togather to get the sum.

Well explained 👍

FAQs on Factors of 87

1.Is 87 a factor tree?

 The number 87 is written on top and two branches are extended. Fill in those branches with a factor pair of the number above, i.e., 87. Continue this process until each branch ends with a prime factor (number). The first two branches of the factor tree of 87 are 3 and 29.
 

2.Is 87 a prime number?

 No, 87 is not a prime number, since 87 has factors other than 1 and itself.
 

3.Is 87 a multiple of 7?

No, 87 is not a multiple of 7, since on division of 87 by 7, we get a remainder of 3.
 

4. Is 87 divisible by 29?

 Yes, 87 is perfectly divisible by 29. 87/29 =3.
 

5.What can 87 be divided by?

 87 can be divided by 1,3,29,87.
 

Important Glossaries for Factors of 87

  • Ratio - Ratio of two numbers compares between them, how many times one number contains the other number. It is expressed as m:n, where m and n are two positive numbers whose ratio is to be shown.
  • Factors - These are numbers that divide the given number without leaving any remainder or the remainder as 0.
  • 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.