What is the Greatest Common Factor of 37842 and 37856?

Greatest common factor (GCF) of 37842 and 37856 is 14.

GCF(37842,37856) = 14

We will now calculate the prime factors of 37842 and 37856, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37842 and 37856.

How to find the GCF of 37842 and 37856?

We will first find the prime factorization of 37842 and 37856. After we will calculate the factors of 37842 and 37856 and find the biggest common factor number .

Step-1: Prime Factorization of 37842

Prime factors of 37842 are 2, 3, 7, 17, 53. Prime factorization of 37842 in exponential form is:

37842 = 2¹ × 3¹ × 7¹ × 17¹ × 53¹

Step-2: Prime Factorization of 37856

Prime factors of 37856 are 2, 7, 13. Prime factorization of 37856 in exponential form is:

37856 = 2⁵ × 7¹ × 13²

Step-3: Factors of 37842

List of positive integer factors of 37842 that divides 37842 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 53, 102, 106, 119, 159, 238, 318, 357, 371, 714, 742, 901, 1113, 1802, 2226, 2703, 5406, 6307, 12614, 18921

Step-4: Factors of 37856

List of positive integer factors of 37856 that divides 37842 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 169, 182, 208, 224, 338, 364, 416, 676, 728, 1183, 1352, 1456, 2366, 2704, 2912, 4732, 5408, 9464, 18928

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37842 and 37856. The biggest common factor number is the GCF number.
So the greatest common factor 37842 and 37856 is 14.

Also check out the Least Common Multiple of 37842 and 37856