What is the Greatest Common Factor of 70500 and 70512?

Greatest common factor (GCF) of 70500 and 70512 is 12.

GCF(70500,70512) = 12

We will now calculate the prime factors of 70500 and 70512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70500 and 70512.

How to find the GCF of 70500 and 70512?

We will first find the prime factorization of 70500 and 70512. After we will calculate the factors of 70500 and 70512 and find the biggest common factor number .

Step-1: Prime Factorization of 70500

Prime factors of 70500 are 2, 3, 5, 47. Prime factorization of 70500 in exponential form is:

70500 = 2² × 3¹ × 5³ × 47¹

Step-2: Prime Factorization of 70512

Prime factors of 70512 are 2, 3, 13, 113. Prime factorization of 70512 in exponential form is:

70512 = 2⁴ × 3¹ × 13¹ × 113¹

Step-3: Factors of 70500

List of positive integer factors of 70500 that divides 70500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 47, 50, 60, 75, 94, 100, 125, 141, 150, 188, 235, 250, 282, 300, 375, 470, 500, 564, 705, 750, 940, 1175, 1410, 1500, 2350, 2820, 3525, 4700, 5875, 7050, 11750, 14100, 17625, 23500, 35250

Step-4: Factors of 70512

List of positive integer factors of 70512 that divides 70500 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 113, 156, 208, 226, 312, 339, 452, 624, 678, 904, 1356, 1469, 1808, 2712, 2938, 4407, 5424, 5876, 8814, 11752, 17628, 23504, 35256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70500 and 70512. The biggest common factor number is the GCF number.
So the greatest common factor 70500 and 70512 is 12.

Also check out the Least Common Multiple of 70500 and 70512