What is the Greatest Common Factor of 46800 and 46814?

Greatest common factor (GCF) of 46800 and 46814 is 2.

GCF(46800,46814) = 2

We will now calculate the prime factors of 46800 and 46814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46800 and 46814.

How to find the GCF of 46800 and 46814?

We will first find the prime factorization of 46800 and 46814. After we will calculate the factors of 46800 and 46814 and find the biggest common factor number .

Step-1: Prime Factorization of 46800

Prime factors of 46800 are 2, 3, 5, 13. Prime factorization of 46800 in exponential form is:

46800 = 2⁴ × 3² × 5² × 13¹

Step-2: Prime Factorization of 46814

Prime factors of 46814 are 2, 89, 263. Prime factorization of 46814 in exponential form is:

46814 = 2¹ × 89¹ × 263¹

Step-3: Factors of 46800

List of positive integer factors of 46800 that divides 46800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 25, 26, 30, 36, 39, 40, 45, 48, 50, 52, 60, 65, 72, 75, 78, 80, 90, 100, 104, 117, 120, 130, 144, 150, 156, 180, 195, 200, 208, 225, 234, 240, 260, 300, 312, 325, 360, 390, 400, 450, 468, 520, 585, 600, 624, 650, 720, 780, 900, 936, 975, 1040, 1170, 1200, 1300, 1560, 1800, 1872, 1950, 2340, 2600, 2925, 3120, 3600, 3900, 4680, 5200, 5850, 7800, 9360, 11700, 15600, 23400

Step-4: Factors of 46814

List of positive integer factors of 46814 that divides 46800 without a remainder.

1, 2, 89, 178, 263, 526, 23407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46800 and 46814. The biggest common factor number is the GCF number.
So the greatest common factor 46800 and 46814 is 2.

Also check out the Least Common Multiple of 46800 and 46814