What is the Greatest Common Factor of 45696 and 45705?

Greatest common factor (GCF) of 45696 and 45705 is 3.

GCF(45696,45705) = 3

We will now calculate the prime factors of 45696 and 45705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45696 and 45705.

How to find the GCF of 45696 and 45705?

We will first find the prime factorization of 45696 and 45705. After we will calculate the factors of 45696 and 45705 and find the biggest common factor number .

Step-1: Prime Factorization of 45696

Prime factors of 45696 are 2, 3, 7, 17. Prime factorization of 45696 in exponential form is:

45696 = 2⁷ × 3¹ × 7¹ × 17¹

Step-2: Prime Factorization of 45705

Prime factors of 45705 are 3, 5, 11, 277. Prime factorization of 45705 in exponential form is:

45705 = 3¹ × 5¹ × 11¹ × 277¹

Step-3: Factors of 45696

List of positive integer factors of 45696 that divides 45696 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 17, 21, 24, 28, 32, 34, 42, 48, 51, 56, 64, 68, 84, 96, 102, 112, 119, 128, 136, 168, 192, 204, 224, 238, 272, 336, 357, 384, 408, 448, 476, 544, 672, 714, 816, 896, 952, 1088, 1344, 1428, 1632, 1904, 2176, 2688, 2856, 3264, 3808, 5712, 6528, 7616, 11424, 15232, 22848

Step-4: Factors of 45705

List of positive integer factors of 45705 that divides 45696 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 277, 831, 1385, 3047, 4155, 9141, 15235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45696 and 45705. The biggest common factor number is the GCF number.
So the greatest common factor 45696 and 45705 is 3.

Also check out the Least Common Multiple of 45696 and 45705