Factors of 75

A number is called a factor of 75 if it completely divides 75 without leaving a remainder. So we can say that the factors of 75 are the divisors of 75. Here, we will learn about the factors of 75 and the prime factors of 75.

  • 75 = 3×5×5 =31×52 is the prime factorization of 75.
  • The factors of 75 are 1, 3, 5, 15, 25 and 75.
  • The prime factors of 75 are 3 and 5.
  • Negative factors of 75 are –1, -3, -5, -15, -25 and –75.

What are the factors of 75?

Let us write the number 75 multiplicatively in all possible ways. We definitely have:

75 = 1×75 

75 = 3×25

75 = 5×15

As there are no other ways we can write 75 multiplicatively, so we will stop right now. So the factors of 75 in pairs are given as follows:

75 = a×b Factors in Pairs (a,b)
75 = 1×75  (1, 75)
75 = 3×25 (3, 25)
75 = 5×15 (5, 15)

Thus the pair factors of 75 are (1, 75), (3, 25), and (5, 15). As all the numbers appearing in pair factors are the factors of 75, we conclude that

The factors of 75 are:

1, 3, 5, 15, 25 and 75.

Number of factors of 75

From above we have calculated the factors of 75 which are 1, 3, 5, 15, 25, and 75.

Thus the total number of factors of 75 is six.

Prime Factors of 75

Note that the factors of 75 are 1, 3, 5, 15,  25, and 75. Among those factors, we observe that only 3 and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 75 are 3 and 5.

Question: What are the factors of 75?

Video Solution:

How to find factors of 75?

Now we will determine the factors of 75 by division method. In this method, we will try to find the numbers that can divide 75 with no remainder. See that

75/1=75 and the remainder is 0.

1 and 75 are factors of 75.

75/3=25 and the remainder is 0.

3 and 25 are factors of 75.

75/5=15 and the remainder is 0.

5 and 15 are factors of 75.

Note that no numbers other than the numbers in violet color can divide 75. So the numbers in violet color, that is, 1, 3, 5, 15, 25, and 75 are the complete list of factors of 75.

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