How to Find GCF of 790/419, 714/840?

GCF of 790/419, 714/840

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 790/419, 714/840 i.e 2/351960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 790/419, 714/840.

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 790/419,714/840?

Given fractions are 790/419,714/840

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 790/419,714/840, numerators are 790,714

Denominators are 419,840

The GCF of 790,714 is 2 .

LCM of 419,840 is 351960.

The greatest common factor of 790/419,714/840 = [GCF of 790,714]/[LCM of 419,840]= 2/351960

Therefore, the GCF of 790/419,714/840 is 2/351960.

Greatest Common Factor of 790,714

To find the highest common factor of 790,714, we have to find the factors of both numbers and list the highest common factor.

The factors of 790 are 1, 2, 5, 10, 79, 158, 395, 790

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

The HCF of 790,714 is 2.

Lets's calculate GCF of 790,714

Greatest Common Factor (GCF) of 790,714 By Common Division

2	790, 714
	395, 357

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

Greatest Common Factor of 790,714 By Matching Biggest Common Factor Method

Now, list down the factors of 790

1,2,5,10,79,158,395,790

Now, list down the factors of 714

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

Greatest Common Factor

We found the factors 790,714 . The biggest common factor number is the GCF number.
So the greatest common factor 790,714 is 2.

Lets's calculate LCM of 419,840

Lowest Common Multiple of 419,840 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 351960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/351960

Therefore, the GCF of Fractions 790/419,714/840 is 2/351960

Least Common Multiple of 419,840 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 419,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(419,840) = 1

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

GCF(419,840) x common factors =1 x 1 = 1

LCM(419,840) = ( 419 × 840 ) / 1

LCM(419,840) = 351960 / 1

LCM(419,840) = 351960

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FAQs on GCF of Fractions of 790/419, 714/840

1. What is the HCF of 790,714?

The HCF of 790,714 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 790/419, 714/840?

Answer: GCF of Numerators as per given numbers 790/419, 714/840 is

GCF of Numerators i.e. for 790,714 is 2

LCM of denominators i.e. for 419,840 is 351960.

Thus, GCF of Fractions is 2/351960.Finally, GCF of Fractions for 790/419, 714/840 is 2/351960.