What are the Factor Pairs of 28?

Factor Pairs of 28

Answer: The factor pairs of 28 are (1, 28), (2, 14), and (4, 7).

Solution: To find the factor pairs of 28, we look for two integers that multiply together to give 28. We systematically check integers starting from 1:

1. We start with the smallest positive integer, 1. We find that $$1 \times 28 = 28$$. So, (1, 28) is a factor pair.

2. Next, we check 2. We find that $$2 \times 14 = 28$$. So, (2, 14) is a factor pair.

3. Next, we check 3. 28 is not divisible by 3 ($$28 \div 3 = 9$$ with a remainder of 1), so 3 is not a factor.

4. Next, we check 4. We find that $$4 \times 7 = 28$$. So, (4, 7) is a factor pair.

5. Next, we check 5. 28 is not divisible by 5, so 5 is not a factor.

6. Next, we check 6. 28 is not divisible by 6, so 6 is not a factor.

7. Next, we check 7. We have already found 7 as part of the pair (4, 7). Since the next integer to check (7) is now greater than or equal to the second number in the last found pair (7), we have found all unique factor pairs. If we were to continue, the pairs would simply be the reverse of those already found \(e.g., (7, 4), (14, 2), (28, 1)\).

Therefore, the unique factor pairs of 28 are (1, 28), (2, 14), and (4, 7).