What is the Greatest Common Factor of 61734 and 61740?

Greatest common factor (GCF) of 61734 and 61740 is 6.

GCF(61734,61740) = 6

We will now calculate the prime factors of 61734 and 61740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61734 and 61740.

How to find the GCF of 61734 and 61740?

We will first find the prime factorization of 61734 and 61740. After we will calculate the factors of 61734 and 61740 and find the biggest common factor number .

Step-1: Prime Factorization of 61734

Prime factors of 61734 are 2, 3, 10289. Prime factorization of 61734 in exponential form is:

61734 = 2¹ × 3¹ × 10289¹

Step-2: Prime Factorization of 61740

Prime factors of 61740 are 2, 3, 5, 7. Prime factorization of 61740 in exponential form is:

61740 = 2² × 3² × 5¹ × 7³

Step-3: Factors of 61734

List of positive integer factors of 61734 that divides 61734 without a remainder.

1, 2, 3, 6, 10289, 20578, 30867

Step-4: Factors of 61740

List of positive integer factors of 61740 that divides 61734 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 49, 60, 63, 70, 84, 90, 98, 105, 126, 140, 147, 180, 196, 210, 245, 252, 294, 315, 343, 420, 441, 490, 588, 630, 686, 735, 882, 980, 1029, 1260, 1372, 1470, 1715, 1764, 2058, 2205, 2940, 3087, 3430, 4116, 4410, 5145, 6174, 6860, 8820, 10290, 12348, 15435, 20580, 30870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61734 and 61740. The biggest common factor number is the GCF number.
So the greatest common factor 61734 and 61740 is 6.

Also check out the Least Common Multiple of 61734 and 61740