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\times 25 = 75.

**List of Pair Factors of 75:**

The list of factors of 75 in pairs are:

- 1 AND 75.
- 3 AND 25.
- 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?**

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

**Calculating the pair factors of 75:**

- When 75 is divided by 1, the remainder is 0 therefore 1 is a factor of 75. Since, 75\div 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\times 75 = 75. - When 75 is divided by 2, the remainder is 1 therefore we conclude that 2 is not a factor of 75.
- When 75 is divided by 3, the remainder is 0 therefore 3 is a factor of 75. Since, 75\div 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\times 25 = 75. - When 75 is divided by 4, the remainder is 3 therefore we conclude that 2 is not a factor of 75.
- When 75 is divided by 5, the remainder is 0 therefore 5 is a factor of 75. Since, 75\div 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\times 15 = 75. - When 75 is divided by 6, the remainder is 3 therefore we conclude that 6 is not a factor of 75.
- When 75 is divided by 7, the remainder is 5 therefore 7 is not a factor of 75.
- When 75 is divided by 8, the remainder is 3 therefore we conclude that 8 is not a factor of 75.
- When 75 is divided by 9, the remainder is 3 therefore 9 is not a factor of 75.
- When 75 is divided by 10, the remainder is 5 therefore we conclude that 10 is not a factor of 75.
- 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 factors pairs found above are the only possible factor pairs.