What is the Greatest Common Factor of 34314 and 34320?

Greatest common factor (GCF) of 34314 and 34320 is 6.

GCF(34314,34320) = 6

We will now calculate the prime factors of 34314 and 34320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34314 and 34320.

How to find the GCF of 34314 and 34320?

We will first find the prime factorization of 34314 and 34320. After we will calculate the factors of 34314 and 34320 and find the biggest common factor number .

Step-1: Prime Factorization of 34314

Prime factors of 34314 are 2, 3, 7, 19, 43. Prime factorization of 34314 in exponential form is:

34314 = 2¹ × 3¹ × 7¹ × 19¹ × 43¹

Step-2: 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-3: Factors of 34314

List of positive integer factors of 34314 that divides 34314 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 43, 57, 86, 114, 129, 133, 258, 266, 301, 399, 602, 798, 817, 903, 1634, 1806, 2451, 4902, 5719, 11438, 17157

Step-4: Factors of 34320

List of positive integer factors of 34320 that divides 34314 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34314 and 34320. The biggest common factor number is the GCF number.
So the greatest common factor 34314 and 34320 is 6.

Also check out the Least Common Multiple of 34314 and 34320