What is the Greatest Common Factor of 38640 and 38657?

Greatest common factor (GCF) of 38640 and 38657 is 1.

GCF(38640,38657) = 1

We will now calculate the prime factors of 38640 and 38657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38640 and 38657.

How to find the GCF of 38640 and 38657?

We will first find the prime factorization of 38640 and 38657. After we will calculate the factors of 38640 and 38657 and find the biggest common factor number .

Step-1: Prime Factorization of 38640

Prime factors of 38640 are 2, 3, 5, 7, 23. Prime factorization of 38640 in exponential form is:

38640 = 2⁴ × 3¹ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 38657

Prime factors of 38657 are 29, 31, 43. Prime factorization of 38657 in exponential form is:

38657 = 29¹ × 31¹ × 43¹

Step-3: Factors of 38640

List of positive integer factors of 38640 that divides 38640 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 105, 112, 115, 120, 138, 140, 161, 168, 184, 210, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 483, 552, 560, 644, 690, 805, 840, 920, 966, 1104, 1288, 1380, 1610, 1680, 1840, 1932, 2415, 2576, 2760, 3220, 3864, 4830, 5520, 6440, 7728, 9660, 12880, 19320

Step-4: Factors of 38657

List of positive integer factors of 38657 that divides 38640 without a remainder.

1, 29, 31, 43, 899, 1247, 1333

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38640 and 38657. The biggest common factor number is the GCF number.
So the greatest common factor 38640 and 38657 is 1.

Also check out the Least Common Multiple of 38640 and 38657