How to Find GCF of 714/676, 770/611?

GCF of 714/676, 770/611

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 714/676, 770/611 i.e 14/31772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/676, 770/611.

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 714/676,770/611?

Given fractions are 714/676,770/611

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 714/676,770/611, numerators are 714,770

Denominators are 676,611

The GCF of 714,770 is 14 .

LCM of 676,611 is 31772.

The greatest common factor of 714/676,770/611 = [GCF of 714,770]/[LCM of 676,611]= 14/31772

Therefore, the GCF of 714/676,770/611 is 14/31772.

Greatest Common Factor of 714,770

To find the highest common factor of 714,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The HCF of 714,770 is 14.

Lets's calculate GCF of 714,770

Greatest Common Factor (GCF) of 714,770 By Common Division

2	714, 770
7	357, 385
	51, 55

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 714,770 By Matching Biggest Common Factor Method

Now, list down the factors of 714

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Now, list down the factors of 770

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Greatest Common Factor

We found the factors 714,770 . The biggest common factor number is the GCF number.
So the greatest common factor 714,770 is 14.

Lets's calculate LCM of 676,611

Lowest Common Multiple of 676,611 using Common Division

13	676, 611
	52, 47

∴ So the LCM of the given numbers is 13 x 52 x 47 = 31772

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/31772

Therefore, the GCF of Fractions 714/676,770/611 is 14/31772

Least Common Multiple of 676,611 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 676,611 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(676,611) = 13

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

GCF(676,611) x common factors =13 x 1 = 13

LCM(676,611) = ( 676 × 611 ) / 13

LCM(676,611) = 413036 / 13

LCM(676,611) = 31772

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FAQs on GCF of Fractions of 714/676, 770/611

1. What is the HCF of 714,770?

The HCF of 714,770 is 14

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 714/676, 770/611?

Answer: GCF of Numerators as per given numbers 714/676, 770/611 is

GCF of Numerators i.e. for 714,770 is 14

LCM of denominators i.e. for 676,611 is 31772.

Thus, GCF of Fractions is 14/31772.Finally, GCF of Fractions for 714/676, 770/611 is 14/31772.