What is the greatest common factor of 120 and 180?

Answer 1

One way to approach this is to look at the difference between 180 and 210, which is 30. The greatest common factor of two numbers cannot be larger than the difference between the two numbers. Since both 180 and 210 are divisible by 30, the greatest common factor is 30.

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

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

The common factors are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the greatest common factor is 30.

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

The prime factors of 180 are 2, 2, 3, 3, and 5.

The prime factors of 210 are 2, 3, 5, and 7.

The prime factors in common are 2, 3, and 5, so the greatest common factor is 2 x 3 x 5 = 30.
The GCF is 30.

Answer 2

The factors of 160 are:

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

The factors of 180 are:

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The common factors are: 1, 2, 4, 5, 10, 20

The Greatest Common Factor (GCF) is: 20

Answer 3

360 is twice 180, so 180 is the greatest common factor. Working this out though:

180 = 2^2 x 3^2 x 5

360 = 2^3 x 3^2 x 5

The highest powers of primes that are present in both the above factorisations are also factors of the greatest common factor:

GCF = 2^2 x 3^2 x 5

= 180

Answer 4

The Greatest Common Factor of 20, 180 is 20.

Answer 5

The greatest common factor of 120 and 180 is 60

Answer 6

Applying Euclid's algorithm, it's the same as the greatest common factor of 120 and 60 (where 60 is the remainder of the division of 180 by 120).

Answer 7

There can only be one 'greatest'.

For 120 and 180, it's 60.

Answer 8

The GCF is 4.

Answer 9

60

Answer 10

It is: 30