What is the Greatest Common Factor of 336 and 354?

Greatest common factor (GCF) of 336 and 354 is 6.

GCF(336,354) = 6

We will now calculate the prime factors of 336 and 354, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 336 and 354.

How to find the GCF of 336 and 354?

We will first find the prime factorization of 336 and 354. After we will calculate the factors of 336 and 354 and find the biggest common factor number .

Step-1: Prime Factorization of 336

Prime factors of 336 are 2, 3, 7. Prime factorization of 336 in exponential form is:

336 = 2⁴ × 3¹ × 7¹

Step-2: 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-3: Factors of 336

List of positive integer factors of 336 that divides 336 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168

Step-4: Factors of 354

List of positive integer factors of 354 that divides 336 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 336 and 354. The biggest common factor number is the GCF number.
So the greatest common factor 336 and 354 is 6.

Also check out the Least Common Multiple of 336 and 354