What is the Greatest Common Factor of 10906 and 10920?

Greatest common factor (GCF) of 10906 and 10920 is 14.

GCF(10906,10920) = 14

We will now calculate the prime factors of 10906 and 10920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10906 and 10920.

How to find the GCF of 10906 and 10920?

We will first find the prime factorization of 10906 and 10920. After we will calculate the factors of 10906 and 10920 and find the biggest common factor number .

Step-1: Prime Factorization of 10906

Prime factors of 10906 are 2, 7, 19, 41. Prime factorization of 10906 in exponential form is:

10906 = 2¹ × 7¹ × 19¹ × 41¹

Step-2: Prime Factorization of 10920

Prime factors of 10920 are 2, 3, 5, 7, 13. Prime factorization of 10920 in exponential form is:

10920 = 2³ × 3¹ × 5¹ × 7¹ × 13¹

Step-3: Factors of 10906

List of positive integer factors of 10906 that divides 10906 without a remainder.

1, 2, 7, 14, 19, 38, 41, 82, 133, 266, 287, 574, 779, 1558, 5453

Step-4: Factors of 10920

List of positive integer factors of 10920 that divides 10906 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 20, 21, 24, 26, 28, 30, 35, 39, 40, 42, 52, 56, 60, 65, 70, 78, 84, 91, 104, 105, 120, 130, 140, 156, 168, 182, 195, 210, 260, 273, 280, 312, 364, 390, 420, 455, 520, 546, 728, 780, 840, 910, 1092, 1365, 1560, 1820, 2184, 2730, 3640, 5460

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10906 and 10920. The biggest common factor number is the GCF number.
So the greatest common factor 10906 and 10920 is 14.

Also check out the Least Common Multiple of 10906 and 10920