What is the Greatest Common Factor of 36960 and 36974?

Greatest common factor (GCF) of 36960 and 36974 is 14.

GCF(36960,36974) = 14

We will now calculate the prime factors of 36960 and 36974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36960 and 36974.

How to find the GCF of 36960 and 36974?

We will first find the prime factorization of 36960 and 36974. After we will calculate the factors of 36960 and 36974 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 36974

Prime factors of 36974 are 2, 7, 19, 139. Prime factorization of 36974 in exponential form is:

36974 = 2¹ × 7¹ × 19¹ × 139¹

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 36974

List of positive integer factors of 36974 that divides 36960 without a remainder.

1, 2, 7, 14, 19, 38, 133, 139, 266, 278, 973, 1946, 2641, 5282, 18487

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36960 and 36974. The biggest common factor number is the GCF number.
So the greatest common factor 36960 and 36974 is 14.

Also check out the Least Common Multiple of 36960 and 36974