What is the greatest common factor of 28 and 35?

What is the greatest common factor of 28 and 35?

• A. 14
• B. 7
• C. 1
• D. 28

Answer: (B)

The greatest common factor is the largest number that divides both numbers exactly. To find it, look at how each number can be broken down into factors. 28 factors as 2 × 2 × 7, and 35 factors as 5 × 7. The only common prime factor they share is 7, so the common factors are 1 and 7. The largest of these is 7, so the greatest common factor is 7. If you list divisors, 28 has 1, 2, 4, 7, 14, 28 and 35 has 1, 5, 7, 35. The intersection is 1 and 7, with 7 being the greatest.

The greatest common factor is the largest number that divides both numbers exactly. To find it, look at how each number can be broken down into factors.

28 factors as 2 × 2 × 7, and 35 factors as 5 × 7. The only common prime factor they share is 7, so the common factors are 1 and 7. The largest of these is 7, so the greatest common factor is 7.

If you list divisors, 28 has 1, 2, 4, 7, 14, 28 and 35 has 1, 5, 7, 35. The intersection is 1 and 7, with 7 being the greatest.