What is the Greatest Common Factor of 61758 and 61764?

Greatest common factor (GCF) of 61758 and 61764 is 6.

GCF(61758,61764) = 6

We will now calculate the prime factors of 61758 and 61764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61758 and 61764.

How to find the GCF of 61758 and 61764?

We will first find the prime factorization of 61758 and 61764. After we will calculate the factors of 61758 and 61764 and find the biggest common factor number .

Step-1: Prime Factorization of 61758

Prime factors of 61758 are 2, 3, 47, 73. Prime factorization of 61758 in exponential form is:

61758 = 2¹ × 3² × 47¹ × 73¹

Step-2: Prime Factorization of 61764

Prime factors of 61764 are 2, 3, 5147. Prime factorization of 61764 in exponential form is:

61764 = 2² × 3¹ × 5147¹

Step-3: Factors of 61758

List of positive integer factors of 61758 that divides 61758 without a remainder.

1, 2, 3, 6, 9, 18, 47, 73, 94, 141, 146, 219, 282, 423, 438, 657, 846, 1314, 3431, 6862, 10293, 20586, 30879

Step-4: Factors of 61764

List of positive integer factors of 61764 that divides 61758 without a remainder.

1, 2, 3, 4, 6, 12, 5147, 10294, 15441, 20588, 30882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61758 and 61764. The biggest common factor number is the GCF number.
So the greatest common factor 61758 and 61764 is 6.

Also check out the Least Common Multiple of 61758 and 61764