What is the Greatest Common Factor of 450 and 462?
Greatest common factor (GCF) of 450 and 462 is 6.
GCF(450,462) = 6
We will now calculate the prime factors of 450 and 462, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 450 and 462.
How to find the GCF of 450 and 462?
We will first find the prime factorization of 450 and 462. After we will calculate the factors of 450 and 462 and find the biggest common factor number .
Step-1: Prime Factorization of 450
Prime factors of 450 are 2, 3, 5. Prime factorization of 450 in exponential form is:
450 = 21 × 32 × 52
Step-2: Prime Factorization of 462
Prime factors of 462 are 2, 3, 7, 11. Prime factorization of 462 in exponential form is:
462 = 21 × 31 × 71 × 111
Step-3: Factors of 450
List of positive integer factors of 450 that divides 450 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225
Step-4: Factors of 462
List of positive integer factors of 462 that divides 450 without a remainder.
1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 450 and 462. The biggest common factor number is the GCF number.
So the greatest common factor 450 and 462 is 6.
Also check out the Least Common Multiple of 450 and 462
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