What is the Greatest Common Factor of 38970 and 38976?

Greatest common factor (GCF) of 38970 and 38976 is 6.

GCF(38970,38976) = 6

We will now calculate the prime factors of 38970 and 38976, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38970 and 38976.

How to find the GCF of 38970 and 38976?

We will first find the prime factorization of 38970 and 38976. After we will calculate the factors of 38970 and 38976 and find the biggest common factor number .

Step-1: Prime Factorization of 38970

Prime factors of 38970 are 2, 3, 5, 433. Prime factorization of 38970 in exponential form is:

38970 = 2¹ × 3² × 5¹ × 433¹

Step-2: Prime Factorization of 38976

Prime factors of 38976 are 2, 3, 7, 29. Prime factorization of 38976 in exponential form is:

38976 = 2⁶ × 3¹ × 7¹ × 29¹

Step-3: Factors of 38970

List of positive integer factors of 38970 that divides 38970 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 433, 866, 1299, 2165, 2598, 3897, 4330, 6495, 7794, 12990, 19485

Step-4: Factors of 38976

List of positive integer factors of 38976 that divides 38970 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 64, 84, 87, 96, 112, 116, 168, 174, 192, 203, 224, 232, 336, 348, 406, 448, 464, 609, 672, 696, 812, 928, 1218, 1344, 1392, 1624, 1856, 2436, 2784, 3248, 4872, 5568, 6496, 9744, 12992, 19488

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38970 and 38976. The biggest common factor number is the GCF number.
So the greatest common factor 38970 and 38976 is 6.

Also check out the Least Common Multiple of 38970 and 38976