What is the Greatest Common Factor of 73749 and 73764?

Greatest common factor (GCF) of 73749 and 73764 is 3.

GCF(73749,73764) = 3

We will now calculate the prime factors of 73749 and 73764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73749 and 73764.

How to find the GCF of 73749 and 73764?

We will first find the prime factorization of 73749 and 73764. After we will calculate the factors of 73749 and 73764 and find the biggest common factor number .

Step-1: Prime Factorization of 73749

Prime factors of 73749 are 3, 13, 31, 61. Prime factorization of 73749 in exponential form is:

73749 = 3¹ × 13¹ × 31¹ × 61¹

Step-2: Prime Factorization of 73764

Prime factors of 73764 are 2, 3, 683. Prime factorization of 73764 in exponential form is:

73764 = 2² × 3³ × 683¹

Step-3: Factors of 73749

List of positive integer factors of 73749 that divides 73749 without a remainder.

1, 3, 13, 31, 39, 61, 93, 183, 403, 793, 1209, 1891, 2379, 5673, 24583

Step-4: Factors of 73764

List of positive integer factors of 73764 that divides 73749 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 683, 1366, 2049, 2732, 4098, 6147, 8196, 12294, 18441, 24588, 36882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73749 and 73764. The biggest common factor number is the GCF number.
So the greatest common factor 73749 and 73764 is 3.

Also check out the Least Common Multiple of 73749 and 73764