What are the Factors of 75 in Pairs?

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.