# What are the Factors of 75 in Pairs?

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We say that a number is a factor of 75 if it properly divides 75 leaving no remainder. The factors of any number always occur in pairs.

A pair of factors of 75 means two numbers which when multiplied together give 75 as the product.

For example, the numbers 3 and 25 are a pair of factors of 75 because

3 x 25 = 75.

### List of Pair Factors of 75:

The list of factors of 75 in pairs are:

1. 1 AND 75.
2. 3 AND 25.
3. 5 AND 15.

This means that 75 has a total of 3 pairs of factors – meaning that there are a total of 6 factors of 75.

### How to find the pair factors of 75?

1. Divide 75 by all numbers between 1 and 10 and calculate the remainder.
2. If the remainder is not zero then discard that number. If the remainder is not zero then that number cannot possible be a factor.
3. If the remainder is zero then the divisor is a factor. The resulting quotient is the other pair factor of 75.
4. Continue this process till you have calculated all the factor pairs of 75.

#### Calculating the pair factors of 75:

1. When 75 is divided by 1, the remainder is 0 therefore 1 is a factor of 75. Since, 75/1 = 75.
• The number 1 is the divisor and 75 is the quotient meaning that (1,75) is the first factor pair. We see that, 1 x 75 = 75.
2. When 75 is divided by 2, the remainder is 1 therefore we conclude that 2 is not a factor of 75.
3. When 75 is divided by 3, the remainder is 0 therefore 3 is a factor of 75. Since, 75/3 = 25.
• The number 3 is the divisor and 25 is the quotient meaning that (3,25) is the second factor pair. We see that, 3 x 25 = 75.
4. When 75 is divided by 4, the remainder is 3 therefore we conclude that 2 is not a factor of 75.
5. When 75 is divided by 5, the remainder is 0 therefore 5 is a factor of 75. Since, 75/5 = 15.
• The number 5 is the divisor and 15 is the quotient meaning that (5,15) is the third factor pair. We see that, 5 x 15 = 75.
6. When 75 is divided by 6, the remainder is 3 therefore we conclude that 6 is not a factor of 75.
7. When 75 is divided by 7, the remainder is 5 therefore 7 is not a factor of 75.
8. When 75 is divided by 8, the remainder is 3 therefore we conclude that 8 is not a factor of 75.
9. When 75 is divided by 9, the remainder is 3 therefore 9 is not a factor of 75.
10. When 75 is divided by 10, the remainder is 5 therefore we conclude that 10 is not a factor of 75.
11. Since we have now checked by finding the remainders when 75 is divided by all numbers lying between 1 and 10 we have completed our search. There are no further factors to be found. So the factor pairs found above are the only possible factor pairs.
Summary
Article Name
What are the Factors of 75 in Pairs?
Description
The list of factors of 75 in pairs is 1 AND 75, 3 AND 25 AND 15.