How to Find GCF of 676/672, 7649/7000?

GCF of 676/672, 7649/7000

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 676/672, 7649/7000 i.e 1/84000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 676/672, 7649/7000.

Enter two or more fractions separated by "commas"

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

What is the GCF of 676/672,7649/7000?

Given fractions are 676/672,7649/7000

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 676/672,7649/7000, numerators are 676,7649

Denominators are 672,7000

The GCF of 676,7649 is 1 .

LCM of 672,7000 is 84000.

The greatest common factor of 676/672,7649/7000 = [GCF of 676,7649]/[LCM of 672,7000]= 1/84000

Therefore, the GCF of 676/672,7649/7000 is 1/84000.

Greatest Common Factor of 676,7649

To find the highest common factor of 676,7649, we have to find the factors of both numbers and list the highest common factor.

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676

The factors of 7649 are 1, 7649

The HCF of 676,7649 is 1.

Lets's calculate GCF of 676,7649

Greatest Common Factor (GCF) of 676,7649 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 676,7649 By Matching Biggest Common Factor Method

Now, list down the factors of 676

1,2,4,13,26,52,169,338,676

Now, list down the factors of 7649

1,7649

Greatest Common Factor

We found the factors 676,7649 . The biggest common factor number is the GCF number.
So the greatest common factor 676,7649 is 1.

Lets's calculate LCM of 672,7000

Lowest Common Multiple of 672,7000 using Common Division

2	672, 7000
2	336, 3500
2	168, 1750
7	84, 875
	12, 125

∴ So the LCM of the given numbers is 2 x 2 x 2 x 7 x 12 x 125 = 84000

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/84000

Therefore, the GCF of Fractions 676/672,7649/7000 is 1/84000

Least Common Multiple of 672,7000 with GCF Formula

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

We need to calculate greatest common factor of 672,7000 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(672,7000) = 56

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

GCF(672,7000) x common factors =56 x 1 = 56

LCM(672,7000) = ( 672 × 7000 ) / 56

LCM(672,7000) = 4704000 / 56

LCM(672,7000) = 84000

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FAQs on GCF of Fractions of 676/672, 7649/7000

1. What is the HCF of 676,7649?

The HCF of 676,7649 is 1

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 676/672, 7649/7000?

Answer: GCF of Numerators as per given numbers 676/672, 7649/7000 is

GCF of Numerators i.e. for 676,7649 is 1

LCM of denominators i.e. for 672,7000 is 84000.

Thus, GCF of Fractions is 1/84000.Finally, GCF of Fractions for 676/672, 7649/7000 is 1/84000.