What is the Greatest Common Factor of 354 and 360?

Greatest common factor (GCF) of 354 and 360 is 6.

GCF(354,360) = 6

We will now calculate the prime factors of 354 and 360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 354 and 360.

How to find the GCF of 354 and 360?

We will first find the prime factorization of 354 and 360. After we will calculate the factors of 354 and 360 and find the biggest common factor number .

Step-1: Prime Factorization of 354

Prime factors of 354 are 2, 3, 59. Prime factorization of 354 in exponential form is:

354 = 2¹ × 3¹ × 59¹

Step-2: Prime Factorization of 360

Prime factors of 360 are 2, 3, 5. Prime factorization of 360 in exponential form is:

360 = 2³ × 3² × 5¹

Step-3: Factors of 354

List of positive integer factors of 354 that divides 354 without a remainder.

1, 2, 3, 6, 59, 118, 177

Step-4: Factors of 360

List of positive integer factors of 360 that divides 354 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 354 and 360. The biggest common factor number is the GCF number.
So the greatest common factor 354 and 360 is 6.

Also check out the Least Common Multiple of 354 and 360