What is the Greatest Common Factor of 11408 and 11424?

Greatest common factor (GCF) of 11408 and 11424 is 16.

GCF(11408,11424) = 16

We will now calculate the prime factors of 11408 and 11424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11408 and 11424.

How to find the GCF of 11408 and 11424?

We will first find the prime factorization of 11408 and 11424. After we will calculate the factors of 11408 and 11424 and find the biggest common factor number .

Step-1: Prime Factorization of 11408

Prime factors of 11408 are 2, 23, 31. Prime factorization of 11408 in exponential form is:

11408 = 2⁴ × 23¹ × 31¹

Step-2: Prime Factorization of 11424

Prime factors of 11424 are 2, 3, 7, 17. Prime factorization of 11424 in exponential form is:

11424 = 2⁵ × 3¹ × 7¹ × 17¹

Step-3: Factors of 11408

List of positive integer factors of 11408 that divides 11408 without a remainder.

1, 2, 4, 8, 16, 23, 31, 46, 62, 92, 124, 184, 248, 368, 496, 713, 1426, 2852, 5704

Step-4: Factors of 11424

List of positive integer factors of 11424 that divides 11408 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 32, 34, 42, 48, 51, 56, 68, 84, 96, 102, 112, 119, 136, 168, 204, 224, 238, 272, 336, 357, 408, 476, 544, 672, 714, 816, 952, 1428, 1632, 1904, 2856, 3808, 5712

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11408 and 11424. The biggest common factor number is the GCF number.
So the greatest common factor 11408 and 11424 is 16.

Also check out the Least Common Multiple of 11408 and 11424