What is the Greatest Common Factor of 53305 and 53312?

Greatest common factor (GCF) of 53305 and 53312 is 7.

GCF(53305,53312) = 7

We will now calculate the prime factors of 53305 and 53312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53305 and 53312.

How to find the GCF of 53305 and 53312?

We will first find the prime factorization of 53305 and 53312. After we will calculate the factors of 53305 and 53312 and find the biggest common factor number .

Step-1: Prime Factorization of 53305

Prime factors of 53305 are 5, 7, 1523. Prime factorization of 53305 in exponential form is:

53305 = 5¹ × 7¹ × 1523¹

Step-2: Prime Factorization of 53312

Prime factors of 53312 are 2, 7, 17. Prime factorization of 53312 in exponential form is:

53312 = 2⁶ × 7² × 17¹

Step-3: Factors of 53305

List of positive integer factors of 53305 that divides 53305 without a remainder.

1, 5, 7, 35, 1523, 7615, 10661

Step-4: Factors of 53312

List of positive integer factors of 53312 that divides 53305 without a remainder.

1, 2, 4, 7, 8, 14, 16, 17, 28, 32, 34, 49, 56, 64, 68, 98, 112, 119, 136, 196, 224, 238, 272, 392, 448, 476, 544, 784, 833, 952, 1088, 1568, 1666, 1904, 3136, 3332, 3808, 6664, 7616, 13328, 26656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53305 and 53312. The biggest common factor number is the GCF number.
So the greatest common factor 53305 and 53312 is 7.

Also check out the Least Common Multiple of 53305 and 53312