What is the Greatest Common Factor of 46656 and 46665?

Greatest common factor (GCF) of 46656 and 46665 is 9.

GCF(46656,46665) = 9

We will now calculate the prime factors of 46656 and 46665, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46656 and 46665.

How to find the GCF of 46656 and 46665?

We will first find the prime factorization of 46656 and 46665. After we will calculate the factors of 46656 and 46665 and find the biggest common factor number .

Step-1: Prime Factorization of 46656

Prime factors of 46656 are 2, 3. Prime factorization of 46656 in exponential form is:

46656 = 2⁶ × 3⁶

Step-2: Prime Factorization of 46665

Prime factors of 46665 are 3, 5, 17, 61. Prime factorization of 46665 in exponential form is:

46665 = 3² × 5¹ × 17¹ × 61¹

Step-3: Factors of 46656

List of positive integer factors of 46656 that divides 46656 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 729, 864, 972, 1296, 1458, 1728, 1944, 2592, 2916, 3888, 5184, 5832, 7776, 11664, 15552, 23328

Step-4: Factors of 46665

List of positive integer factors of 46665 that divides 46656 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 61, 85, 153, 183, 255, 305, 549, 765, 915, 1037, 2745, 3111, 5185, 9333, 15555

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46656 and 46665. The biggest common factor number is the GCF number.
So the greatest common factor 46656 and 46665 is 9.

Also check out the Least Common Multiple of 46656 and 46665