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GCF of 280/408, 671/714

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 280/408, 671/714 i.e 1/2856 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/408, 671/714.

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 280/408,671/714?

Given fractions are 280/408,671/714

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 280/408,671/714, numerators are 280,671

Denominators are 408,714

The GCF of 280,671 is 1 .

LCM of 408,714 is 2856.

The greatest common factor of 280/408,671/714 = [GCF of 280,671]/[LCM of 408,714]= 1/2856

Therefore, the GCF of 280/408,671/714 is 1/2856.

Greatest Common Factor of 280,671

To find the highest common factor of 280,671, we have to find the factors of both numbers and list the highest common factor.

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

The factors of 671 are 1, 11, 61, 671

The HCF of 280,671 is 1.

Lets's calculate GCF of 280,671

Greatest Common Factor (GCF) of 280,671 By Common Division

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

Greatest Common Factor of 280,671 By Matching Biggest Common Factor Method

Greatest Common Factor of 280,671 By Matching Biggest Common Factor Method

Now, list down the factors of 280

:

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

Now, list down the factors of 671

:

1,11,61,671

Greatest Common Factor

We found the factors 280,671 . The biggest common factor number is the GCF number.
So the greatest common factor 280,671 is 1.

Lets's calculate LCM of 408,714

Lowest Common Multiple of 408,714 using Common Division

2 408, 714
3 204, 357
17 68, 119
4, 7

∴ So the LCM of the given numbers is 2 x 3 x 17 x 4 x 7 = 2856

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2856

Therefore, the GCF of Fractions 280/408,671/714 is 1/2856

Least Common Multiple of 408,714 with GCF Formula

Least Common Multiple of 408,714 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 408,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(408,714) = 102

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

GCF(408,714) x common factors =102 x 1 = 102

LCM(408,714) = ( 408 × 714 ) / 102

LCM(408,714) = 291312 / 102

LCM(408,714) = 2856


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FAQs on GCF of Fractions of 280/408, 671/714

1. What is the HCF of 280,671?

The HCF of 280,671 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 280/408, 671/714?

Answer: GCF of Numerators as per given numbers 280/408, 671/714 is

GCF of Numerators i.e. for 280,671 is 1

LCM of denominators i.e. for 408,714 is 2856.

Thus, GCF of Fractions is 1/2856.Finally, GCF of Fractions for 280/408, 671/714 is 1/2856.