What is the Greatest Common Factor of 53730 and 53742?

Greatest common factor (GCF) of 53730 and 53742 is 6.

GCF(53730,53742) = 6

We will now calculate the prime factors of 53730 and 53742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53730 and 53742.

How to find the GCF of 53730 and 53742?

We will first find the prime factorization of 53730 and 53742. After we will calculate the factors of 53730 and 53742 and find the biggest common factor number .

Step-1: Prime Factorization of 53730

Prime factors of 53730 are 2, 3, 5, 199. Prime factorization of 53730 in exponential form is:

53730 = 2¹ × 3³ × 5¹ × 199¹

Step-2: Prime Factorization of 53742

Prime factors of 53742 are 2, 3, 13, 53. Prime factorization of 53742 in exponential form is:

53742 = 2¹ × 3¹ × 13² × 53¹

Step-3: Factors of 53730

List of positive integer factors of 53730 that divides 53730 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 199, 270, 398, 597, 995, 1194, 1791, 1990, 2985, 3582, 5373, 5970, 8955, 10746, 17910, 26865

Step-4: Factors of 53742

List of positive integer factors of 53742 that divides 53730 without a remainder.

1, 2, 3, 6, 13, 26, 39, 53, 78, 106, 159, 169, 318, 338, 507, 689, 1014, 1378, 2067, 4134, 8957, 17914, 26871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53730 and 53742. The biggest common factor number is the GCF number.
So the greatest common factor 53730 and 53742 is 6.

Also check out the Least Common Multiple of 53730 and 53742