What is the Greatest Common Factor of 53805 and 53822?

Greatest common factor (GCF) of 53805 and 53822 is 17.

GCF(53805,53822) = 17

We will now calculate the prime factors of 53805 and 53822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53805 and 53822.

How to find the GCF of 53805 and 53822?

We will first find the prime factorization of 53805 and 53822. After we will calculate the factors of 53805 and 53822 and find the biggest common factor number .

Step-1: Prime Factorization of 53805

Prime factors of 53805 are 3, 5, 17, 211. Prime factorization of 53805 in exponential form is:

53805 = 3¹ × 5¹ × 17¹ × 211¹

Step-2: Prime Factorization of 53822

Prime factors of 53822 are 2, 17, 1583. Prime factorization of 53822 in exponential form is:

53822 = 2¹ × 17¹ × 1583¹

Step-3: Factors of 53805

List of positive integer factors of 53805 that divides 53805 without a remainder.

1, 3, 5, 15, 17, 51, 85, 211, 255, 633, 1055, 3165, 3587, 10761, 17935

Step-4: Factors of 53822

List of positive integer factors of 53822 that divides 53805 without a remainder.

1, 2, 17, 34, 1583, 3166, 26911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53805 and 53822. The biggest common factor number is the GCF number.
So the greatest common factor 53805 and 53822 is 17.

Also check out the Least Common Multiple of 53805 and 53822