What is the Greatest Common Factor of 5705 and 5712?

Greatest common factor (GCF) of 5705 and 5712 is 7.

GCF(5705,5712) = 7

We will now calculate the prime factors of 5705 and 5712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5705 and 5712.

How to find the GCF of 5705 and 5712?

We will first find the prime factorization of 5705 and 5712. After we will calculate the factors of 5705 and 5712 and find the biggest common factor number .

Step-1: Prime Factorization of 5705

Prime factors of 5705 are 5, 7, 163. Prime factorization of 5705 in exponential form is:

5705 = 5¹ × 7¹ × 163¹

Step-2: Prime Factorization of 5712

Prime factors of 5712 are 2, 3, 7, 17. Prime factorization of 5712 in exponential form is:

5712 = 2⁴ × 3¹ × 7¹ × 17¹

Step-3: Factors of 5705

List of positive integer factors of 5705 that divides 5705 without a remainder.

1, 5, 7, 35, 163, 815, 1141

Step-4: Factors of 5712

List of positive integer factors of 5712 that divides 5705 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 34, 42, 48, 51, 56, 68, 84, 102, 112, 119, 136, 168, 204, 238, 272, 336, 357, 408, 476, 714, 816, 952, 1428, 1904, 2856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5705 and 5712. The biggest common factor number is the GCF number.
So the greatest common factor 5705 and 5712 is 7.

Also check out the Least Common Multiple of 5705 and 5712