What is the Greatest Common Factor of 35700 and 35712?

Greatest common factor (GCF) of 35700 and 35712 is 12.

GCF(35700,35712) = 12

We will now calculate the prime factors of 35700 and 35712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35700 and 35712.

How to find the GCF of 35700 and 35712?

We will first find the prime factorization of 35700 and 35712. After we will calculate the factors of 35700 and 35712 and find the biggest common factor number .

Step-1: Prime Factorization of 35700

Prime factors of 35700 are 2, 3, 5, 7, 17. Prime factorization of 35700 in exponential form is:

35700 = 2² × 3¹ × 5² × 7¹ × 17¹

Step-2: Prime Factorization of 35712

Prime factors of 35712 are 2, 3, 31. Prime factorization of 35712 in exponential form is:

35712 = 2⁷ × 3² × 31¹

Step-3: Factors of 35700

List of positive integer factors of 35700 that divides 35700 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 25, 28, 30, 34, 35, 42, 50, 51, 60, 68, 70, 75, 84, 85, 100, 102, 105, 119, 140, 150, 170, 175, 204, 210, 238, 255, 300, 340, 350, 357, 420, 425, 476, 510, 525, 595, 700, 714, 850, 1020, 1050, 1190, 1275, 1428, 1700, 1785, 2100, 2380, 2550, 2975, 3570, 5100, 5950, 7140, 8925, 11900, 17850

Step-4: Factors of 35712

List of positive integer factors of 35712 that divides 35700 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 31, 32, 36, 48, 62, 64, 72, 93, 96, 124, 128, 144, 186, 192, 248, 279, 288, 372, 384, 496, 558, 576, 744, 992, 1116, 1152, 1488, 1984, 2232, 2976, 3968, 4464, 5952, 8928, 11904, 17856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35700 and 35712. The biggest common factor number is the GCF number.
So the greatest common factor 35700 and 35712 is 12.

Also check out the Least Common Multiple of 35700 and 35712