What is the Greatest Common Factor of 36960 and 36971?

Greatest common factor (GCF) of 36960 and 36971 is 11.

GCF(36960,36971) = 11

We will now calculate the prime factors of 36960 and 36971, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36960 and 36971.

How to find the GCF of 36960 and 36971?

We will first find the prime factorization of 36960 and 36971. After we will calculate the factors of 36960 and 36971 and find the biggest common factor number .

Step-1: Prime Factorization of 36960

Prime factors of 36960 are 2, 3, 5, 7, 11. Prime factorization of 36960 in exponential form is:

36960 = 2⁵ × 3¹ × 5¹ × 7¹ × 11¹

Step-2: Prime Factorization of 36971

Prime factors of 36971 are 11, 3361. Prime factorization of 36971 in exponential form is:

36971 = 11¹ × 3361¹

Step-3: Factors of 36960

List of positive integer factors of 36960 that divides 36960 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 28, 30, 32, 33, 35, 40, 42, 44, 48, 55, 56, 60, 66, 70, 77, 80, 84, 88, 96, 105, 110, 112, 120, 132, 140, 154, 160, 165, 168, 176, 210, 220, 224, 231, 240, 264, 280, 308, 330, 336, 352, 385, 420, 440, 462, 480, 528, 560, 616, 660, 672, 770, 840, 880, 924, 1056, 1120, 1155, 1232, 1320, 1540, 1680, 1760, 1848, 2310, 2464, 2640, 3080, 3360, 3696, 4620, 5280, 6160, 7392, 9240, 12320, 18480

Step-4: Factors of 36971

List of positive integer factors of 36971 that divides 36960 without a remainder.

1, 11, 3361

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36960 and 36971. The biggest common factor number is the GCF number.
So the greatest common factor 36960 and 36971 is 11.

Also check out the Least Common Multiple of 36960 and 36971