What is the Greatest Common Factor of 336 and 350?

Greatest common factor (GCF) of 336 and 350 is 14.

GCF(336,350) = 14

We will now calculate the prime factors of 336 and 350, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 336 and 350.

How to find the GCF of 336 and 350?

We will first find the prime factorization of 336 and 350. After we will calculate the factors of 336 and 350 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 350

Prime factors of 350 are 2, 5, 7. Prime factorization of 350 in exponential form is:

350 = 2¹ × 5² × 7¹

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 350

List of positive integer factors of 350 that divides 336 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 336 and 350. The biggest common factor number is the GCF number.
So the greatest common factor 336 and 350 is 14.

Also check out the Least Common Multiple of 336 and 350