253 LearnersLast updated on May 26th, 2025
Factors of 87
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.
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.
Mistake 1
Misconception and confusion about factors with that of multiples.
Factors are way different from multiples. You need to understand it clearly that factors are integers which divide a given number evenly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 87 Examples
Problem 1
Find the GCF of 87 and 58
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.
Problem 2
Find the smallest number which, when divided by 29 and 87, leaves a remainder 5 in each case.
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.
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?
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.
Problem 4
Find the smallest number that is divisible by 3,29.
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.
Problem 5
What is the sum of the factors of 87 and 88?
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.
FAQs on Factors of 87
1.Is 87 a factor tree?
2.Is 87 a prime number?
3.Is 87 a multiple of 7?
4. Is 87 divisible by 29?
5.What can 87 be divided by?
6.How can children in Qatar use numbers in everyday life to understand Factors of 87?
7.What are some fun ways kids in Qatar can practice Factors of 87 with numbers?
8.What role do numbers and Factors of 87 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 87 skills?
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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About BrightChamps in Qatar
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.
