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What is the Greatest Common Factor of 83160 and 83174?

Greatest common factor (GCF) of 83160 and 83174 is 14.

GCF(83160,83174) = 14

We will now calculate the prime factors of 83160 and 83174, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83160 and 83174.

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How to find the GCF of 83160 and 83174?

We will first find the prime factorization of 83160 and 83174. After we will calculate the factors of 83160 and 83174 and find the biggest common factor number .

Step-1: Prime Factorization of 83160

Prime factors of 83160 are 2, 3, 5, 7, 11. Prime factorization of 83160 in exponential form is:

83160 = 23 × 33 × 51 × 71 × 111

Step-2: Prime Factorization of 83174

Prime factors of 83174 are 2, 7, 13, 457. Prime factorization of 83174 in exponential form is:

83174 = 21 × 71 × 131 × 4571

Step-3: Factors of 83160

List of positive integer factors of 83160 that divides 83160 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 40, 42, 44, 45, 54, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 105, 108, 110, 120, 126, 132, 135, 140, 154, 165, 168, 180, 189, 198, 210, 216, 220, 231, 252, 264, 270, 280, 297, 308, 315, 330, 360, 378, 385, 396, 420, 440, 462, 495, 504, 540, 594, 616, 630, 660, 693, 756, 770, 792, 840, 924, 945, 990, 1080, 1155, 1188, 1260, 1320, 1386, 1485, 1512, 1540, 1848, 1890, 1980, 2079, 2310, 2376, 2520, 2772, 2970, 3080, 3465, 3780, 3960, 4158, 4620, 5544, 5940, 6930, 7560, 8316, 9240, 10395, 11880, 13860, 16632, 20790, 27720, 41580

Step-4: Factors of 83174

List of positive integer factors of 83174 that divides 83160 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 457, 914, 3199, 5941, 6398, 11882, 41587

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83160 and 83174. The biggest common factor number is the GCF number.
So the greatest common factor 83160 and 83174 is 14.

Also check out the Least Common Multiple of 83160 and 83174