Factors of 87
87 is one of those special two-digit numbers that have two prime numbers as its only pair factors, besides 1 and the number itself. Factors of 87 are the numbers which, when multiplied in pairs, give the product as 87. These factors can be negative as well. It also is a composite number, which means that it has several factors. In this lesson, we will calculate the factors of 87, prime factors of 87, and factors of 87 in pairs along with solved examples for a better understanding.
Factors of 87: 1, 3, and 29
Prime Factorization of 87: 87 = 1 x 3 x 29
| 1. | What Are the Factors of 87? |
| 2. | How to Calculate the Factors of 87? |
| 3. | Factors of 87 by Prime Factorization |
| 4. | Factors of 87 in Pairs |
| 5. | FAQs on Factors of 87 |
What Are the Factors of 87?
Factors of 87 are the numbers that leave the remainder 0 when 87 is being divided by them. Let's first see the numbers that completely divide 87. The positive numbers are 1, 3, 29, and 87 which divide 87 completely. The negative numbers are -1, -3, -29, and -87 which divide 87 completely.
How to Calculate the Factors of 87
To calculate the factors of 87, we can use different methods like prime factorization and the division method. In prime factorization, we express 87 as a product of its prime factors and in the division method, we see what numbers divide 87 exactly. The prime factorization of 87 is using a factor tree method as shown below:
The rectangle represents a composite number and circles represent prime numbers.
So, prime factorization of 87 = 3 × 29
Now that we have done the prime factorization of 87, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.
Important Notes
- The factors of 87 are 1, 3, 29, and 87.
- 87 is an odd number and has all factors as an odd number. This property holds true for every odd number.
Factors of 87 in Pairs
Pair factors are the factors of a number given in pairs which, when multiplied together, give that original number.
The pair factors of 87 would be the two numbers which, when multiplied together, result in the value 87.
The following table represents the pair factors of 87.
| Product | Pair factors |
| 1 × 87 | (1,87) |
| 3 × 29 | (3,29) |
Since the product of two negative numbers is positive.
So, (-1,-87) and (-3,-29) are also factor pairs of 87.
Factors of 87 by Prime Factorization
We begin by searching for the smallest prime number which can divide 87 leaving the remainder 0.
As 87 is an odd number, it will not be divisible by 2.
Now, the sum of digits in the number 87 is 8 + 7 = 15, which is divisible by 3.
So, 87 will also be divisible by 3.
We obtain 29 on dividing 87 by 3. The factors of 29 are 1 and 29 itself. Since it has only two factors, it's a prime number. So, we have 3 and 29 as the prime factors of 87.
FAQs on factors of 87
1. Is 87 a prime number and why?
No, 87 is not a prime number as it has 4 factors.
A number is called prime if it has only two factors which are 1 and the number itself.
2. What is the greatest common factor (GCF) of 87 and 95?
The factors of 87 are 1, 3, 29, and 87.
The factors of 95 are 1, 5, 19, and 95.
They don't have any common factor other than 1.
So, the GCF of 87 and 95 = 1
3. What are the 4 factors of 87?
the factors of 87 are 1, 3, 29, and 87.
4. Is 87 prime or composite?
87 is a composite number as it has 4 factors. Any number having more than 2 factors is called a composite number.