Factors of 31 Using Prime Factorization
What are the Factors of 31?
Factors of 31 will be divisors that exactly divide the number 31 leaving zero as the remainder. In this article we will learn to find the list of all factors, prime factors and factor pairs of 31. Factors can be negative as well as positive.
Factors | Factor pairs | Prime Factor |
|---|---|---|
1, 31 | (1, 31) | 31 |
List of Factors
To find out the total number of factors of 31 we need to do a divisibility test.
Divisor | Is the number a factor of 31 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all number | 1 x 31 = 31 |
2 | No, 31 is odd | ------- |
3 | No, 3 + 1 = 4 is not divisible by 3 | ------- |
4 | No, as 31 \(\div\) 4 = 7 and the remainder = 3 | ------- |
5 | No, the ones digit is neither 0 nor 5 | ------- |
6 | No, 31 is neither divisible by 2 nor with 3 | ------- |
7 | No, as 31 \(\div\) 7 = 4 and the remainder = 3 | ------- |
8 | No, as 31 \(\div\) 8 = 3 and the remainder = 7 | ------- |
9 | No, Since 31 is not divisible by 3 | ------- |
10 | No, as 31 \(\div\) 10 = 3 and the remainder = 1 | ------- |
11 | No, as 31 \(\div\) 11 = 2 and the remainder = 9 | ------- |
We can keep checking the division of 31 till we reach 31 itself. This will tell us that none of the numbers divide 31 completely, except 1 and 31 itself. This suggests that 31 is a prime number with only two factors, 1 and 31 itself.
The list of factors: 1 and 31.
Factor Pair
A factor pair of a number is a set of any of its two of its factors such that their product is the number itself.
Positive factor of 31 | Positive factor pair of 31 |
|---|---|
1 x 31 = 31 | (1, 31) |
Prime Factor of 31 are: 1 and 31
Read More:
Rapid Recall
31 has only two factors 1 and 31.
Solved Factors of 31 Examples
Example 1: You want to organize 31 pictures into a rectangular array on a wall. How many different arrays can you make ?
Solution:
To find the number of array you can make, find the number of factor pairs of 31.
There is only one factor pair of 31 which is (1, 31).
you can use each factor pair to make 2 arrays.
So there are two ways two organize the picture in a rectangular array:
a. One row and 31 columns.
b. One column and 31 rows.
Example 2: Find the five positive multiples of 31.
Solution:
The first five positive multiples of 31 are:
1 x 31 = 31
2 x 31 = 62
3 x 31 = 93
4 x 31 = 124
5 x 31 = 155
Example 3: Find the factors of 62.
Solution:
Factorization of 62 : 1 x 2 x 31
An even number is completely divisible by 2 but an odd number is not completely divisible by 2.
Factors are the numbers that we can multiply together to get the product. If one of the factors is an even number, then its product with other factors produces an even number or in other words any multiple of even numbers is always an even number. This is why an odd number can not have even factors.
For example :
15 is an odd number and its factors are 1, 3, 5 and 15. Therefore, we can clearly see that an odd number has odd factors.
Even numbers can have odd factors.
For example:
The factors of 26 are 1, 2 and 13. Here 1 and 13 are odd factors.
The factors of 52 are 1, 2, 4 and 13. Here 13 is an odd factor.
The factors of 36 are 1, 2, 4, 6, 9, 12 and 18. Here 9 is an odd factor.
No, factors must be less than the number itself. Therefore, the number of factors of any number is finite.
Factors of any number will be divisors which exactly divide the number leaving zero as the remainder.
Prime factors are also factors and the only difference is that they are prime numbers.
For example:
Factors of 45 are 1, 3, 5, 9, 15 and 45.
The numbers written above are called the factors of 45. However, 3 and 5 are prime numbers, and are therefore called the prime factors of 45.