Factors of 75 Using Prime Factorization
What are the Factors of 75?
The factors of 75 are integers that divide 75 without leaving any remainder. In other words, the factors of 75 divide 75 exactly.
Example: 5 is a factor of 75 because when we divide 75 by 5, it gives us 15 as the quotient and 0 as the remainder. Here, the quotient, 15, is also a factor of 75.
The Factors of 75
So, to check if any number is a factor of 75, divide 75 by that number and check if the remainder is 0 or not.
Factor List of 75
The factors of 75 are 1, 3, 5, 15, 25, and 75.
The Prime Factorization of 75
The factor tree of 75 can be written as:
The prime factorization of 75 is 3 × 5 × 5 = 3 × \(5^2\).
This indicates that 3 and 5 are the prime factors of 75.
The Factor Pairs of 75
The factor pair of 75 is a pair of factors that, when multiplied, result in 75.
For example, (3, 25) is a factor pair of 75, as 3 × 25 = 75
Positive factor pairs of 75
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Rapid Recall
Solved Factors of 75 Examples
Example 1: Find the common factors of 60 and 75.
Solution:
The factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The factors of 75: 1, 3, 5, 15, 25, and 75.
So, the common factors of 60 and 75 are 1, 3, 5, and 15.
Example 2: How many factors does 75 have?
Solution:
The factors of 75: 1, 3, 5, 15, 25, and 75.
So, there are 6 factors of 75.
Example 3:
A school library has a collection of 75 books on the history of America. The books are to be arranged equally on 15 shelves. How many books will be placed on each shelf?
Solution:
75 books are to be equally arranged on 15 shelves.
To find how many books can be placed on each shelf, we will divide 75 by 15, that is,
\(\frac{75}{15}\) = 5 R0
As a result, 5 books can be placed on each shelf.
When you divide 75 by 7, it will give 5 as a remainder, that is, 7 does not divide 75 exactly. Hence, 7 is not a factor of 75.
Numbers that divide 75 exactly, that is, leave zero as the remainder, are known as the factors of 75.
The factors of 75 are 1, 3, 5, 15, 25, and 75.
Hence, the sum of all the factors of 75 is
= 1 + 3 + 5 + 15 + 25 + 75 = 124
Hence, the sum is 124.
Yes, 75 is a composite number as it has factors other than one and itself. It has factors of 3, 5, 15, and 25, other than 1 and 75.
The factors of 75 are 1, 3, 5, 15, 25, and 75.
So, the smallest factor of 75 is 1, and the greatest factor is 75 itself.