What is the Greatest Common Factor of 1152 and 1170?

Greatest common factor (GCF) of 1152 and 1170 is 18.

GCF(1152,1170) = 18

We will now calculate the prime factors of 1152 and 1170, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1152 and 1170.

How to find the GCF of 1152 and 1170?

We will first find the prime factorization of 1152 and 1170. After we will calculate the factors of 1152 and 1170 and find the biggest common factor number .

Step-1: Prime Factorization of 1152

Prime factors of 1152 are 2, 3. Prime factorization of 1152 in exponential form is:

1152 = 2⁷ × 3²

Step-2: Prime Factorization of 1170

Prime factors of 1170 are 2, 3, 5, 13. Prime factorization of 1170 in exponential form is:

1170 = 2¹ × 3² × 5¹ × 13¹

Step-3: Factors of 1152

List of positive integer factors of 1152 that divides 1152 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576

Step-4: Factors of 1170

List of positive integer factors of 1170 that divides 1152 without a remainder.

1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1152 and 1170. The biggest common factor number is the GCF number.
So the greatest common factor 1152 and 1170 is 18.

Also check out the Least Common Multiple of 1152 and 1170