What is the Greatest Common Factor of 61824 and 61838?

Greatest common factor (GCF) of 61824 and 61838 is 14.

GCF(61824,61838) = 14

We will now calculate the prime factors of 61824 and 61838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61824 and 61838.

How to find the GCF of 61824 and 61838?

We will first find the prime factorization of 61824 and 61838. After we will calculate the factors of 61824 and 61838 and find the biggest common factor number .

Step-1: Prime Factorization of 61824

Prime factors of 61824 are 2, 3, 7, 23. Prime factorization of 61824 in exponential form is:

61824 = 2⁷ × 3¹ × 7¹ × 23¹

Step-2: Prime Factorization of 61838

Prime factors of 61838 are 2, 7, 631. Prime factorization of 61838 in exponential form is:

61838 = 2¹ × 7² × 631¹

Step-3: Factors of 61824

List of positive integer factors of 61824 that divides 61824 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 32, 42, 46, 48, 56, 64, 69, 84, 92, 96, 112, 128, 138, 161, 168, 184, 192, 224, 276, 322, 336, 368, 384, 448, 483, 552, 644, 672, 736, 896, 966, 1104, 1288, 1344, 1472, 1932, 2208, 2576, 2688, 2944, 3864, 4416, 5152, 7728, 8832, 10304, 15456, 20608, 30912

Step-4: Factors of 61838

List of positive integer factors of 61838 that divides 61824 without a remainder.

1, 2, 7, 14, 49, 98, 631, 1262, 4417, 8834, 30919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61824 and 61838. The biggest common factor number is the GCF number.
So the greatest common factor 61824 and 61838 is 14.

Also check out the Least Common Multiple of 61824 and 61838