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GCF of 454/496, 682/731

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 454/496, 682/731 i.e 2/362576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 454/496, 682/731.

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 454/496,682/731?

Given fractions are 454/496,682/731

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 454/496,682/731, numerators are 454,682

Denominators are 496,731

The GCF of 454,682 is 2 .

LCM of 496,731 is 362576.

The greatest common factor of 454/496,682/731 = [GCF of 454,682]/[LCM of 496,731]= 2/362576

Therefore, the GCF of 454/496,682/731 is 2/362576.

Greatest Common Factor of 454,682

To find the highest common factor of 454,682, we have to find the factors of both numbers and list the highest common factor.

The factors of 454 are 1, 2, 227, 454

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

The HCF of 454,682 is 2.

Lets's calculate GCF of 454,682

Greatest Common Factor (GCF) of 454,682 By Common Division

2 454, 682
227, 341

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

Greatest Common Factor of 454,682 By Matching Biggest Common Factor Method

Greatest Common Factor of 454,682 By Matching Biggest Common Factor Method

Now, list down the factors of 454

:

1,2,227,454

Now, list down the factors of 682

:

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

Greatest Common Factor

We found the factors 454,682 . The biggest common factor number is the GCF number.
So the greatest common factor 454,682 is 2.

Lets's calculate LCM of 496,731

Lowest Common Multiple of 496,731 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 362576

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/362576

Therefore, the GCF of Fractions 454/496,682/731 is 2/362576

Least Common Multiple of 496,731 with GCF Formula

Least Common Multiple of 496,731 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 496,731 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(496,731) = 1

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

GCF(496,731) x common factors =1 x 1 = 1

LCM(496,731) = ( 496 × 731 ) / 1

LCM(496,731) = 362576 / 1

LCM(496,731) = 362576


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FAQs on GCF of Fractions of 454/496, 682/731

1. What is the HCF of 454,682?

The HCF of 454,682 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 454/496, 682/731?

Answer: GCF of Numerators as per given numbers 454/496, 682/731 is

GCF of Numerators i.e. for 454,682 is 2

LCM of denominators i.e. for 496,731 is 362576.

Thus, GCF of Fractions is 2/362576.Finally, GCF of Fractions for 454/496, 682/731 is 2/362576.