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GCF of 678/649, 682/675

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 678/649, 682/675 i.e 2/438075 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/649, 682/675.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 678/649,682/675?

Given fractions are 678/649,682/675

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 678/649,682/675, numerators are 678,682

Denominators are 649,675

The GCF of 678,682 is 2 .

LCM of 649,675 is 438075.

The greatest common factor of 678/649,682/675 = [GCF of 678,682]/[LCM of 649,675]= 2/438075

Therefore, the GCF of 678/649,682/675 is 2/438075.

Greatest Common Factor of 678,682

To find the highest common factor of 678,682, we have to find the factors of both numbers and list the highest common factor.

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The HCF of 678,682 is 2.

Lets's calculate GCF of 678,682

Greatest Common Factor (GCF) of 678,682 By Common Division

2 678, 682
339, 341

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 678,682 By Matching Biggest Common Factor Method

Greatest Common Factor of 678,682 By Matching Biggest Common Factor Method

Now, list down the factors of 678

:

1,2,3,6,113,226,339,678

Now, list down the factors of 682

:

1,2,11,22,31,62,341,682

Greatest Common Factor

We found the factors 678,682 . The biggest common factor number is the GCF number.
So the greatest common factor 678,682 is 2.

Lets's calculate LCM of 649,675

Lowest Common Multiple of 649,675 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 438075

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/438075

Therefore, the GCF of Fractions 678/649,682/675 is 2/438075

Least Common Multiple of 649,675 with GCF Formula

Least Common Multiple of 649,675 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 649,675 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(649,675) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(649,675) x common factors =1 x 1 = 1

LCM(649,675) = ( 649 × 675 ) / 1

LCM(649,675) = 438075 / 1

LCM(649,675) = 438075


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FAQs on GCF of Fractions of 678/649, 682/675

1. What is the HCF of 678,682?

The HCF of 678,682 is 2

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 678/649, 682/675?

Answer: GCF of Numerators as per given numbers 678/649, 682/675 is

GCF of Numerators i.e. for 678,682 is 2

LCM of denominators i.e. for 649,675 is 438075.

Thus, GCF of Fractions is 2/438075.Finally, GCF of Fractions for 678/649, 682/675 is 2/438075.