What is the Greatest Common Factor of 52080 and 52096?

Greatest common factor (GCF) of 52080 and 52096 is 16.

GCF(52080,52096) = 16

We will now calculate the prime factors of 52080 and 52096, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52080 and 52096.

How to find the GCF of 52080 and 52096?

We will first find the prime factorization of 52080 and 52096. After we will calculate the factors of 52080 and 52096 and find the biggest common factor number .

Step-1: Prime Factorization of 52080

Prime factors of 52080 are 2, 3, 5, 7, 31. Prime factorization of 52080 in exponential form is:

52080 = 2⁴ × 3¹ × 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 52096

Prime factors of 52096 are 2, 11, 37. Prime factorization of 52096 in exponential form is:

52096 = 2⁷ × 11¹ × 37¹

Step-3: Factors of 52080

List of positive integer factors of 52080 that divides 52080 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 31, 35, 40, 42, 48, 56, 60, 62, 70, 80, 84, 93, 105, 112, 120, 124, 140, 155, 168, 186, 210, 217, 240, 248, 280, 310, 336, 372, 420, 434, 465, 496, 560, 620, 651, 744, 840, 868, 930, 1085, 1240, 1302, 1488, 1680, 1736, 1860, 2170, 2480, 2604, 3255, 3472, 3720, 4340, 5208, 6510, 7440, 8680, 10416, 13020, 17360, 26040

Step-4: Factors of 52096

List of positive integer factors of 52096 that divides 52080 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 37, 44, 64, 74, 88, 128, 148, 176, 296, 352, 407, 592, 704, 814, 1184, 1408, 1628, 2368, 3256, 4736, 6512, 13024, 26048

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52080 and 52096. The biggest common factor number is the GCF number.
So the greatest common factor 52080 and 52096 is 16.

Also check out the Least Common Multiple of 52080 and 52096