To find the factors of 75, we need to identify all the whole numbers that divide 75 without leaving a remainder. Let’s break it down step by step in a simple way.
What Are the Factors of 75?
To find all the factors of 75, start from 1 and go up to 75.
Try dividing 75 by each number. If it divides evenly (no remainder), then that number is a factor.
Try 1: 75 ÷ 1 = 75 so, 1 is a factor.
Try 2: 75 ÷ 2 = 37.5 Not a whole number. So, 2 is not a factor.
Try 3: 75 ÷ 3 = 25 Yes! 3 is a factor.
Try 4: 75 ÷ 4 = 18.75 Not a factor.
Try 5: 75 ÷ 5 = 15 Yes! 5 is a factor.
List All the Factors
Factors of 75 = 1, 3, 5, 15, 25, 75
Find Factor Pairs of 75
Positive Pair Factors of 75
Let’s look at all the positive numbers that can be multiplied together to give 75.
1 × 75 = 75 → So, (1, 75) is a pair factor
3 × 25 = 75 → So, (3, 25) is a pair factor
5 × 15 = 75 → So, (5, 15) is a pair factor
Positive Pair Factors of 75 = (1, 75), (3, 25), (5, 15)
Negative Pair Factors of 75
Now let’s talk about negative pair factors.
When you multiply two negative numbers, you also get a positive number!
So we can create pairs like this:
–1 × –75 = 75 → So, (–1, –75) is a pair factor
–3 × –25 = 75 → So, (–3, –25) is a pair factor
–5 × –15 = 75 → So, (–5, –15) is a pair factor
Negative Pair Factors of 75 = (–1, –75), (–3, –25), (–5, –15)
Prime Factorization of 75
Another way to find factors is by breaking 75 into its prime factors:
Divide 75 by the smallest prime number (3):
75 ÷ 3 = 25, 3 is a prime factor.
Now, factorize 25:
25 ÷ 5 = 5, 5 is a prime factor.
Finally, factorize 5:
5 ÷ 5 = 1, 5 is again a prime factor.
So, the prime factorization of 75 is:
75 = 3 × 5 × 5 or 3 × 52
