What is the Greatest Common Factor of 65730 and 65736?

Greatest common factor (GCF) of 65730 and 65736 is 6.

GCF(65730,65736) = 6

We will now calculate the prime factors of 65730 and 65736, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65730 and 65736.

How to find the GCF of 65730 and 65736?

We will first find the prime factorization of 65730 and 65736. After we will calculate the factors of 65730 and 65736 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 65736

Prime factors of 65736 are 2, 3, 11, 83. Prime factorization of 65736 in exponential form is:

65736 = 2³ × 3² × 11¹ × 83¹

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 65736

List of positive integer factors of 65736 that divides 65730 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 83, 88, 99, 132, 166, 198, 249, 264, 332, 396, 498, 664, 747, 792, 913, 996, 1494, 1826, 1992, 2739, 2988, 3652, 5478, 5976, 7304, 8217, 10956, 16434, 21912, 32868

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65730 and 65736. The biggest common factor number is the GCF number.
So the greatest common factor 65730 and 65736 is 6.

Also check out the Least Common Multiple of 65730 and 65736