What is the Greatest Common Factor of 74100 and 74112?

Greatest common factor (GCF) of 74100 and 74112 is 12.

GCF(74100,74112) = 12

We will now calculate the prime factors of 74100 and 74112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74100 and 74112.

How to find the GCF of 74100 and 74112?

We will first find the prime factorization of 74100 and 74112. After we will calculate the factors of 74100 and 74112 and find the biggest common factor number .

Step-1: Prime Factorization of 74100

Prime factors of 74100 are 2, 3, 5, 13, 19. Prime factorization of 74100 in exponential form is:

74100 = 2² × 3¹ × 5² × 13¹ × 19¹

Step-2: Prime Factorization of 74112

Prime factors of 74112 are 2, 3, 193. Prime factorization of 74112 in exponential form is:

74112 = 2⁷ × 3¹ × 193¹

Step-3: Factors of 74100

List of positive integer factors of 74100 that divides 74100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 19, 20, 25, 26, 30, 38, 39, 50, 52, 57, 60, 65, 75, 76, 78, 95, 100, 114, 130, 150, 156, 190, 195, 228, 247, 260, 285, 300, 325, 380, 390, 475, 494, 570, 650, 741, 780, 950, 975, 988, 1140, 1235, 1300, 1425, 1482, 1900, 1950, 2470, 2850, 2964, 3705, 3900, 4940, 5700, 6175, 7410, 12350, 14820, 18525, 24700, 37050

Step-4: Factors of 74112

List of positive integer factors of 74112 that divides 74100 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 193, 384, 386, 579, 772, 1158, 1544, 2316, 3088, 4632, 6176, 9264, 12352, 18528, 24704, 37056

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74100 and 74112. The biggest common factor number is the GCF number.
So the greatest common factor 74100 and 74112 is 12.

Also check out the Least Common Multiple of 74100 and 74112