What is the Greatest Common Factor of 38415 and 38430?

Greatest common factor (GCF) of 38415 and 38430 is 15.

GCF(38415,38430) = 15

We will now calculate the prime factors of 38415 and 38430, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38415 and 38430.

How to find the GCF of 38415 and 38430?

We will first find the prime factorization of 38415 and 38430. After we will calculate the factors of 38415 and 38430 and find the biggest common factor number .

Step-1: Prime Factorization of 38415

Prime factors of 38415 are 3, 5, 13, 197. Prime factorization of 38415 in exponential form is:

38415 = 3¹ × 5¹ × 13¹ × 197¹

Step-2: Prime Factorization of 38430

Prime factors of 38430 are 2, 3, 5, 7, 61. Prime factorization of 38430 in exponential form is:

38430 = 2¹ × 3² × 5¹ × 7¹ × 61¹

Step-3: Factors of 38415

List of positive integer factors of 38415 that divides 38415 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 197, 591, 985, 2561, 2955, 7683, 12805

Step-4: Factors of 38430

List of positive integer factors of 38430 that divides 38415 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 61, 63, 70, 90, 105, 122, 126, 183, 210, 305, 315, 366, 427, 549, 610, 630, 854, 915, 1098, 1281, 1830, 2135, 2562, 2745, 3843, 4270, 5490, 6405, 7686, 12810, 19215

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38415 and 38430. The biggest common factor number is the GCF number.
So the greatest common factor 38415 and 38430 is 15.

Also check out the Least Common Multiple of 38415 and 38430