What is the Greatest Common Factor of 35100 and 35112?

Greatest common factor (GCF) of 35100 and 35112 is 12.

GCF(35100,35112) = 12

We will now calculate the prime factors of 35100 and 35112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35100 and 35112.

How to find the GCF of 35100 and 35112?

We will first find the prime factorization of 35100 and 35112. After we will calculate the factors of 35100 and 35112 and find the biggest common factor number .

Step-1: Prime Factorization of 35100

Prime factors of 35100 are 2, 3, 5, 13. Prime factorization of 35100 in exponential form is:

35100 = 2² × 3³ × 5² × 13¹

Step-2: Prime Factorization of 35112

Prime factors of 35112 are 2, 3, 7, 11, 19. Prime factorization of 35112 in exponential form is:

35112 = 2³ × 3¹ × 7¹ × 11¹ × 19¹

Step-3: Factors of 35100

List of positive integer factors of 35100 that divides 35100 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 27, 30, 36, 39, 45, 50, 52, 54, 60, 65, 75, 78, 90, 100, 108, 117, 130, 135, 150, 156, 180, 195, 225, 234, 260, 270, 300, 325, 351, 390, 450, 468, 540, 585, 650, 675, 702, 780, 900, 975, 1170, 1300, 1350, 1404, 1755, 1950, 2340, 2700, 2925, 3510, 3900, 5850, 7020, 8775, 11700, 17550

Step-4: Factors of 35112

List of positive integer factors of 35112 that divides 35100 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 19, 21, 22, 24, 28, 33, 38, 42, 44, 56, 57, 66, 76, 77, 84, 88, 114, 132, 133, 152, 154, 168, 209, 228, 231, 264, 266, 308, 399, 418, 456, 462, 532, 616, 627, 798, 836, 924, 1064, 1254, 1463, 1596, 1672, 1848, 2508, 2926, 3192, 4389, 5016, 5852, 8778, 11704, 17556

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35100 and 35112. The biggest common factor number is the GCF number.
So the greatest common factor 35100 and 35112 is 12.

Also check out the Least Common Multiple of 35100 and 35112