What is the Greatest Common Factor of 34320 and 34333?

Greatest common factor (GCF) of 34320 and 34333 is 13.

GCF(34320,34333) = 13

We will now calculate the prime factors of 34320 and 34333, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34320 and 34333.

How to find the GCF of 34320 and 34333?

We will first find the prime factorization of 34320 and 34333. After we will calculate the factors of 34320 and 34333 and find the biggest common factor number .

Step-1: Prime Factorization of 34320

Prime factors of 34320 are 2, 3, 5, 11, 13. Prime factorization of 34320 in exponential form is:

34320 = 2⁴ × 3¹ × 5¹ × 11¹ × 13¹

Step-2: Prime Factorization of 34333

Prime factors of 34333 are 13, 19, 139. Prime factorization of 34333 in exponential form is:

34333 = 13¹ × 19¹ × 139¹

Step-3: Factors of 34320

List of positive integer factors of 34320 that divides 34320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 15, 16, 20, 22, 24, 26, 30, 33, 39, 40, 44, 48, 52, 55, 60, 65, 66, 78, 80, 88, 104, 110, 120, 130, 132, 143, 156, 165, 176, 195, 208, 220, 240, 260, 264, 286, 312, 330, 390, 429, 440, 520, 528, 572, 624, 660, 715, 780, 858, 880, 1040, 1144, 1320, 1430, 1560, 1716, 2145, 2288, 2640, 2860, 3120, 3432, 4290, 5720, 6864, 8580, 11440, 17160

Step-4: Factors of 34333

List of positive integer factors of 34333 that divides 34320 without a remainder.

1, 13, 19, 139, 247, 1807, 2641

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34320 and 34333. The biggest common factor number is the GCF number.
So the greatest common factor 34320 and 34333 is 13.

Also check out the Least Common Multiple of 34320 and 34333