What is the Greatest Common Factor of 76734 and 76749?

Greatest common factor (GCF) of 76734 and 76749 is 3.

GCF(76734,76749) = 3

We will now calculate the prime factors of 76734 and 76749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76734 and 76749.

How to find the GCF of 76734 and 76749?

We will first find the prime factorization of 76734 and 76749. After we will calculate the factors of 76734 and 76749 and find the biggest common factor number .

Step-1: Prime Factorization of 76734

Prime factors of 76734 are 2, 3, 7, 29. Prime factorization of 76734 in exponential form is:

76734 = 2¹ × 3³ × 7² × 29¹

Step-2: Prime Factorization of 76749

Prime factors of 76749 are 3, 25583. Prime factorization of 76749 in exponential form is:

76749 = 3¹ × 25583¹

Step-3: Factors of 76734

List of positive integer factors of 76734 that divides 76734 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 29, 42, 49, 54, 58, 63, 87, 98, 126, 147, 174, 189, 203, 261, 294, 378, 406, 441, 522, 609, 783, 882, 1218, 1323, 1421, 1566, 1827, 2646, 2842, 3654, 4263, 5481, 8526, 10962, 12789, 25578, 38367

Step-4: Factors of 76749

List of positive integer factors of 76749 that divides 76734 without a remainder.

1, 3, 25583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76734 and 76749. The biggest common factor number is the GCF number.
So the greatest common factor 76734 and 76749 is 3.

Also check out the Least Common Multiple of 76734 and 76749