What is the Greatest Common Factor of 70686 and 70700?

Greatest common factor (GCF) of 70686 and 70700 is 14.

GCF(70686,70700) = 14

We will now calculate the prime factors of 70686 and 70700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70686 and 70700.

How to find the GCF of 70686 and 70700?

We will first find the prime factorization of 70686 and 70700. After we will calculate the factors of 70686 and 70700 and find the biggest common factor number .

Step-1: Prime Factorization of 70686

Prime factors of 70686 are 2, 3, 7, 11, 17. Prime factorization of 70686 in exponential form is:

70686 = 2¹ × 3³ × 7¹ × 11¹ × 17¹

Step-2: Prime Factorization of 70700

Prime factors of 70700 are 2, 5, 7, 101. Prime factorization of 70700 in exponential form is:

70700 = 2² × 5² × 7¹ × 101¹

Step-3: Factors of 70686

List of positive integer factors of 70686 that divides 70686 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 17, 18, 21, 22, 27, 33, 34, 42, 51, 54, 63, 66, 77, 99, 102, 119, 126, 153, 154, 187, 189, 198, 231, 238, 297, 306, 357, 374, 378, 459, 462, 561, 594, 693, 714, 918, 1071, 1122, 1309, 1386, 1683, 2079, 2142, 2618, 3213, 3366, 3927, 4158, 5049, 6426, 7854, 10098, 11781, 23562, 35343

Step-4: Factors of 70700

List of positive integer factors of 70700 that divides 70686 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 101, 140, 175, 202, 350, 404, 505, 700, 707, 1010, 1414, 2020, 2525, 2828, 3535, 5050, 7070, 10100, 14140, 17675, 35350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70686 and 70700. The biggest common factor number is the GCF number.
So the greatest common factor 70686 and 70700 is 14.

Also check out the Least Common Multiple of 70686 and 70700