What is the greatest common factor of 78 and 93?

Answer 1

One way to approach this is to look at the difference between 78 and 93, which is 15. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. Neither 78 nor 93 are divisible by 15, so consider the other factors of 15, which are 1, 3, and 5. Neither number is divisible by the next largest factor, 5, so try 3. Since both 78 and 93 are divisible by 3, the greatest common factor is 3.

Another way to determine the greatest common factor is to find all the factors of the numbers and compare them.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78.

The factors of 93 are 1, 3, 31, and 93.

The common factors are 1 and 3. Therefore, the greatest common factor is 3.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 78 are 2, 3, and 13.

The prime factors of 93 are 3 and 31.

The prime factors in common are a single 3, so the greatest common factor is 3.