GCF of 126 and 168 (Greatest Common Factor)

"Greatest Common Factor" Calculator
Greatest Common Factor of
and

What is the Greatest Common Divisor of 126 and 168?

Answer

GCF of 126 and 168 is
42

(Forty-two)

Finding GCF for 126 and 168 using all factors (divisors) listing

The first method to find GCF for numbers 126 and 168 is to list all factors for both numbers and pick the highest common one:

All factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

All factors of 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

So the Greatest Common Factor for 126 and 168 is 42

Finding GCF for 126 and 168 by Prime Factorization

The second method to find GCF for numbers 126 and 168 is to list all Prime Factors for both numbers and multiply the common ones:

All Prime Factors of 126: 2, 3, 3, 7

All Prime Factors of 168: 2, 2, 2, 3, 7

As we can see there are Prime Factors common to both numbers: 2, 3, 7

Now we need to multiply them to find GCF: 2 × 3 × 7 = 42

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About "Greatest Common Factor" Calculator

This calculator will help you find the greatest common factor (GCF) of two numbers. For example, it can help you find out what is the Greatest Common Divisor of 126 and 168? (The answer is: 42). Select the first number (e.g. '126') and the second number (e.g. '168'). After that hit the 'Calculate' button.
Greatest Common Factor (GCF) also known as the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) - it is the largest positive integer that divides each of the integers with zero remainder.
"Greatest Common Factor" Calculator
Greatest Common Factor of
and

GCF Table

Number 1Number 2GCF
1261539
12615414
1261551
1261566
1261571
1261582
1261593
1261602
1261617
12616218
1261631
1261642
1261653
1261662
1261671
12616842
1261691
1261702
1261719
1261722
1261731
1261746
1261757
1261762
1261773
1261782
1261791
12618018
1261811
12618214

FAQ

What is the Greatest Common Divisor of 126 and 168?

GCF of 126 and 168 is 42

How to find the GCF of 126 and 168?

You can find the GCF of 126 and 168 by listing all factors of both numbers and picking the greatest common one, or by prime factorization. The GCF of 126 and 168 is 42.

What prime factors do 126 and 168 share?

The prime factorizations of 126 and 168 have 2 × 3 × 7 in common, and multiplying those shared primes gives 42 — exactly the greatest common factor.

How does the GCF reduce the fraction 126/168?

Divide the numerator and the denominator by the GCF 42: 126 ÷ 42 = 3 and 168 ÷ 42 = 4. So 126/168 in lowest terms is 3/4.

See Also