How to Find GCF of 756/969, 676/656?

GCF of 756/969, 676/656

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 756/969, 676/656 i.e 4/635664 easily. The following is the detailed procedure to determine the greatest common factor of fractions 756/969, 676/656.

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 756/969,676/656?

Given fractions are 756/969,676/656

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 756/969,676/656, numerators are 756,676

Denominators are 969,656

The GCF of 756,676 is 4 .

LCM of 969,656 is 635664.

The greatest common factor of 756/969,676/656 = [GCF of 756,676]/[LCM of 969,656]= 4/635664

Therefore, the GCF of 756/969,676/656 is 4/635664.

Greatest Common Factor of 756,676

To find the highest common factor of 756,676, we have to find the factors of both numbers and list the highest common factor.

The factors of 756 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756

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

The HCF of 756,676 is 4.

Lets's calculate GCF of 756,676

Greatest Common Factor (GCF) of 756,676 By Common Division

2	756, 676
2	378, 338
	189, 169

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 756,676 By Matching Biggest Common Factor Method

Now, list down the factors of 756

1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756

Now, list down the factors of 676

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

Greatest Common Factor

We found the factors 756,676 . The biggest common factor number is the GCF number.
So the greatest common factor 756,676 is 4.

Lets's calculate LCM of 969,656

Lowest Common Multiple of 969,656 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 635664

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/635664

Therefore, the GCF of Fractions 756/969,676/656 is 4/635664

Least Common Multiple of 969,656 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 969,656 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(969,656) = 1

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

GCF(969,656) x common factors =1 x 1 = 1

LCM(969,656) = ( 969 × 656 ) / 1

LCM(969,656) = 635664 / 1

LCM(969,656) = 635664

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FAQs on GCF of Fractions of 756/969, 676/656

1. What is the HCF of 756,676?

The HCF of 756,676 is 4

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 756/969, 676/656?

Answer: GCF of Numerators as per given numbers 756/969, 676/656 is

GCF of Numerators i.e. for 756,676 is 4

LCM of denominators i.e. for 969,656 is 635664.

Thus, GCF of Fractions is 4/635664.Finally, GCF of Fractions for 756/969, 676/656 is 4/635664.