What is the Greatest Common Factor of 59742 and 59760?

Greatest common factor (GCF) of 59742 and 59760 is 18.

GCF(59742,59760) = 18

We will now calculate the prime factors of 59742 and 59760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59742 and 59760.

How to find the GCF of 59742 and 59760?

We will first find the prime factorization of 59742 and 59760. After we will calculate the factors of 59742 and 59760 and find the biggest common factor number .

Step-1: Prime Factorization of 59742

Prime factors of 59742 are 2, 3, 3319. Prime factorization of 59742 in exponential form is:

59742 = 2¹ × 3² × 3319¹

Step-2: Prime Factorization of 59760

Prime factors of 59760 are 2, 3, 5, 83. Prime factorization of 59760 in exponential form is:

59760 = 2⁴ × 3² × 5¹ × 83¹

Step-3: Factors of 59742

List of positive integer factors of 59742 that divides 59742 without a remainder.

1, 2, 3, 6, 9, 18, 3319, 6638, 9957, 19914, 29871

Step-4: Factors of 59760

List of positive integer factors of 59760 that divides 59742 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 83, 90, 120, 144, 166, 180, 240, 249, 332, 360, 415, 498, 664, 720, 747, 830, 996, 1245, 1328, 1494, 1660, 1992, 2490, 2988, 3320, 3735, 3984, 4980, 5976, 6640, 7470, 9960, 11952, 14940, 19920, 29880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59742 and 59760. The biggest common factor number is the GCF number.
So the greatest common factor 59742 and 59760 is 18.

Also check out the Least Common Multiple of 59742 and 59760