What is the Greatest Common Factor of 65730 and 65740?

Greatest common factor (GCF) of 65730 and 65740 is 10.

GCF(65730,65740) = 10

We will now calculate the prime factors of 65730 and 65740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65730 and 65740.

How to find the GCF of 65730 and 65740?

We will first find the prime factorization of 65730 and 65740. After we will calculate the factors of 65730 and 65740 and find the biggest common factor number .

Step-1: Prime Factorization of 65730

Prime factors of 65730 are 2, 3, 5, 7, 313. Prime factorization of 65730 in exponential form is:

65730 = 2¹ × 3¹ × 5¹ × 7¹ × 313¹

Step-2: Prime Factorization of 65740

Prime factors of 65740 are 2, 5, 19, 173. Prime factorization of 65740 in exponential form is:

65740 = 2² × 5¹ × 19¹ × 173¹

Step-3: Factors of 65730

List of positive integer factors of 65730 that divides 65730 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 313, 626, 939, 1565, 1878, 2191, 3130, 4382, 4695, 6573, 9390, 10955, 13146, 21910, 32865

Step-4: Factors of 65740

List of positive integer factors of 65740 that divides 65730 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 173, 190, 346, 380, 692, 865, 1730, 3287, 3460, 6574, 13148, 16435, 32870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65730 and 65740. The biggest common factor number is the GCF number.
So the greatest common factor 65730 and 65740 is 10.

Also check out the Least Common Multiple of 65730 and 65740