What is the Greatest Common Factor of 39564 and 39578?

Greatest common factor (GCF) of 39564 and 39578 is 14.

GCF(39564,39578) = 14

We will now calculate the prime factors of 39564 and 39578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39564 and 39578.

How to find the GCF of 39564 and 39578?

We will first find the prime factorization of 39564 and 39578. After we will calculate the factors of 39564 and 39578 and find the biggest common factor number .

Step-1: Prime Factorization of 39564

Prime factors of 39564 are 2, 3, 7, 157. Prime factorization of 39564 in exponential form is:

39564 = 2² × 3² × 7¹ × 157¹

Step-2: Prime Factorization of 39578

Prime factors of 39578 are 2, 7, 11, 257. Prime factorization of 39578 in exponential form is:

39578 = 2¹ × 7¹ × 11¹ × 257¹

Step-3: Factors of 39564

List of positive integer factors of 39564 that divides 39564 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 157, 252, 314, 471, 628, 942, 1099, 1413, 1884, 2198, 2826, 3297, 4396, 5652, 6594, 9891, 13188, 19782

Step-4: Factors of 39578

List of positive integer factors of 39578 that divides 39564 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 257, 514, 1799, 2827, 3598, 5654, 19789

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39564 and 39578. The biggest common factor number is the GCF number.
So the greatest common factor 39564 and 39578 is 14.

Also check out the Least Common Multiple of 39564 and 39578