What is the Greatest Common Factor of 35616 and 35630?

Greatest common factor (GCF) of 35616 and 35630 is 14.

GCF(35616,35630) = 14

We will now calculate the prime factors of 35616 and 35630, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35616 and 35630.

How to find the GCF of 35616 and 35630?

We will first find the prime factorization of 35616 and 35630. After we will calculate the factors of 35616 and 35630 and find the biggest common factor number .

Step-1: Prime Factorization of 35616

Prime factors of 35616 are 2, 3, 7, 53. Prime factorization of 35616 in exponential form is:

35616 = 2⁵ × 3¹ × 7¹ × 53¹

Step-2: Prime Factorization of 35630

Prime factors of 35630 are 2, 5, 7, 509. Prime factorization of 35630 in exponential form is:

35630 = 2¹ × 5¹ × 7¹ × 509¹

Step-3: Factors of 35616

List of positive integer factors of 35616 that divides 35616 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 53, 56, 84, 96, 106, 112, 159, 168, 212, 224, 318, 336, 371, 424, 636, 672, 742, 848, 1113, 1272, 1484, 1696, 2226, 2544, 2968, 4452, 5088, 5936, 8904, 11872, 17808

Step-4: Factors of 35630

List of positive integer factors of 35630 that divides 35616 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 509, 1018, 2545, 3563, 5090, 7126, 17815

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35616 and 35630. The biggest common factor number is the GCF number.
So the greatest common factor 35616 and 35630 is 14.

Also check out the Least Common Multiple of 35616 and 35630