What are the Factors of 87?
Factors of 87 are the numbers that divide 87 evenly, that is, with no remainder. If we divide 87 by a natural number that will give us 0 as a remainder then the number is a factor of 87. The numbers that do not divide 87 completely or evenly are not factors of 87.
The number 87 has a total of four factors, which are, 1, 3, 29 and 87.
[Note: If a number is divided by its factor then the quotient obtained is also a factor of that number.]
List of Factors of 87
Divisibility rules and division facts can be applied to determine whether a number is a factor of 87 or not.
We can stop the derivation of factors with this step as the multiplication equations will start to repeat for larger numbers. So, the factors of 87 are the multiplicands of each multiplication equation. Since there are 2 multiplication equations with unique multiplicands, the number 87 has four factors, which are, 1, 3, 29 and 87.
Prime Factorization of 87
Prime factorization of a number implies that we express the number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of that number.
The factor tree of 87 that is represented as an image describes the prime factorization of 87.
So, the prime factorization of 87 is, 87 = 3 x 29
Factor Pairs of 87
The factor pair of a number is a set of two factors of that number whose product is the number itself.
The factor pairs of 87 are the pairs of its factors whose product is 87. For example: (3, 29) is a factor pair of 87, since ‘3 x 29 = 87’.
Factor of Pairs 87
Read More:
Solved Factors of 87 Examples
Example 1: Find the common factors of 87 and 90.
Solution:
Factors of 87 = 1, 3, 29 and 87.
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Therefore, the common factors of 87 and 90 are 1 and 3.
Example 2: Find the greatest common factor of 60 and 87.
Solution:
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
Factors of 87 = 1, 3, 29 and 87
The common factors of 60 and 87 are 1 and 3.
Therefore, the greatest common factor of 60 and 87 is 3.
Example 3: What is the difference between the prime factors of 87?
Solution :
Factors of 87 = 1, 3, 29 and 87.
The prime factors of 87 are 3 and 29.
Hence, the difference between the prime factors of 87 is, 29 – 3 = 26.
Example 4 : John distributed 87 chocolates among 29 friends. How many chocolates did each friend get?
Solution:
Total number of chocolates = 87
Total number of friends = 29
To find the number of chocolates that each friend got, we just need to know the factor pair of 87 which includes 29. The factor pair is (3, 29).
Therefore, each friend got 3 chocolates.
If we divide 87 by 19 then we get 11 as remainder, that is, 19 does not divide 87 completely. So 19 is not a factor of 87.
The factors of 87 are 1, 3, 29 and 87.
Sum of factors = 1 + 3 + 29 + 87 = 120.
The factor pairs of 87 are the pairs of numbers whose product is 87. The factor pairs of 87 are (1, 87) and (3, 29).
A number which has exactly two factors which are 1 and the number itself is known as a prime number.
The number 87 has more than two factors, hence, it is a composite number.