What is the greatest common factor of 142 and 148?

Answer 1

The GCF of 142 and 148 is 2.

One way to approach this is to look at the difference between 142 and 148, which is 6. 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. The factors of 6 are 1, 2, 3, and 6. Since neither 142 and 148 are divisible by 6, try the next largest factor of 6. Since neither 142 nor 148 are divisible by 3, try the next largest factor. Since both numbers are divisible by 2, the greatest common factor is 2.

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

The factors of 142 are 1, 2, 71, and 142.

The factors of 148 are 1, 2, 4, 37, 74, and 148.

The common factors are 1 and 2. Therefore, the greatest common factor is 2.

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

The prime factors of 142 are 2 and 71.

The prime factors of 148 are 2, 2, and 37.

The prime factors in common are a single 2, so the greatest common factor is 2.