What is the Greatest Common Factor of 61698 and 61712?

Greatest common factor (GCF) of 61698 and 61712 is 14.

GCF(61698,61712) = 14

We will now calculate the prime factors of 61698 and 61712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61698 and 61712.

How to find the GCF of 61698 and 61712?

We will first find the prime factorization of 61698 and 61712. After we will calculate the factors of 61698 and 61712 and find the biggest common factor number .

Step-1: Prime Factorization of 61698

Prime factors of 61698 are 2, 3, 7, 13, 113. Prime factorization of 61698 in exponential form is:

61698 = 2¹ × 3¹ × 7¹ × 13¹ × 113¹

Step-2: Prime Factorization of 61712

Prime factors of 61712 are 2, 7, 19, 29. Prime factorization of 61712 in exponential form is:

61712 = 2⁴ × 7¹ × 19¹ × 29¹

Step-3: Factors of 61698

List of positive integer factors of 61698 that divides 61698 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 113, 182, 226, 273, 339, 546, 678, 791, 1469, 1582, 2373, 2938, 4407, 4746, 8814, 10283, 20566, 30849

Step-4: Factors of 61712

List of positive integer factors of 61712 that divides 61698 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 29, 38, 56, 58, 76, 112, 116, 133, 152, 203, 232, 266, 304, 406, 464, 532, 551, 812, 1064, 1102, 1624, 2128, 2204, 3248, 3857, 4408, 7714, 8816, 15428, 30856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61698 and 61712. The biggest common factor number is the GCF number.
So the greatest common factor 61698 and 61712 is 14.

Also check out the Least Common Multiple of 61698 and 61712