What is the Greatest Common Factor of 53669 and 53680?

Greatest common factor (GCF) of 53669 and 53680 is 11.

GCF(53669,53680) = 11

We will now calculate the prime factors of 53669 and 53680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53669 and 53680.

How to find the GCF of 53669 and 53680?

We will first find the prime factorization of 53669 and 53680. After we will calculate the factors of 53669 and 53680 and find the biggest common factor number .

Step-1: Prime Factorization of 53669

Prime factors of 53669 are 7, 11, 17, 41. Prime factorization of 53669 in exponential form is:

53669 = 7¹ × 11¹ × 17¹ × 41¹

Step-2: Prime Factorization of 53680

Prime factors of 53680 are 2, 5, 11, 61. Prime factorization of 53680 in exponential form is:

53680 = 2⁴ × 5¹ × 11¹ × 61¹

Step-3: Factors of 53669

List of positive integer factors of 53669 that divides 53669 without a remainder.

1, 7, 11, 17, 41, 77, 119, 187, 287, 451, 697, 1309, 3157, 4879, 7667

Step-4: Factors of 53680

List of positive integer factors of 53680 that divides 53669 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 61, 80, 88, 110, 122, 176, 220, 244, 305, 440, 488, 610, 671, 880, 976, 1220, 1342, 2440, 2684, 3355, 4880, 5368, 6710, 10736, 13420, 26840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53669 and 53680. The biggest common factor number is the GCF number.
So the greatest common factor 53669 and 53680 is 11.

Also check out the Least Common Multiple of 53669 and 53680