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GCF of 354/46, 826/700

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 354/46, 826/700 i.e 118/16100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 354/46, 826/700.

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 354/46,826/700?

Given fractions are 354/46,826/700

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 354/46,826/700, numerators are 354,826

Denominators are 46,700

The GCF of 354,826 is 118 .

LCM of 46,700 is 16100.

The greatest common factor of 354/46,826/700 = [GCF of 354,826]/[LCM of 46,700]= 118/16100

Therefore, the GCF of 354/46,826/700 is 118/16100.

Greatest Common Factor of 354,826

To find the highest common factor of 354,826, we have to find the factors of both numbers and list the highest common factor.

The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354

The factors of 826 are 1, 2, 7, 14, 59, 118, 413, 826

The HCF of 354,826 is 118.

Lets's calculate GCF of 354,826

Greatest Common Factor (GCF) of 354,826 By Common Division

2 354, 826
59 177, 413
3, 7

∴ So the GCF of the given numbers is 2 x 59 = 118

Greatest Common Factor of 354,826 By Matching Biggest Common Factor Method

Greatest Common Factor of 354,826 By Matching Biggest Common Factor Method

Now, list down the factors of 354

:

1,2,3,6,59,118,177,354

Now, list down the factors of 826

:

1,2,7,14,59,118,413,826

Greatest Common Factor

We found the factors 354,826 . The biggest common factor number is the GCF number.
So the greatest common factor 354,826 is 118.

Lets's calculate LCM of 46,700

Lowest Common Multiple of 46,700 using Common Division

2 46, 700
23, 350

∴ So the LCM of the given numbers is 2 x 23 x 350 = 16100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 118/16100

Therefore, the GCF of Fractions 354/46,826/700 is 118/16100

Least Common Multiple of 46,700 with GCF Formula

Least Common Multiple of 46,700 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 46,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(46,700) = 2

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

GCF(46,700) x common factors =2 x 1 = 2

LCM(46,700) = ( 46 × 700 ) / 2

LCM(46,700) = 32200 / 2

LCM(46,700) = 16100


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FAQs on GCF of Fractions of 354/46, 826/700

1. What is the HCF of 354,826?

The HCF of 354,826 is 118

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 354/46, 826/700?

Answer: GCF of Numerators as per given numbers 354/46, 826/700 is

GCF of Numerators i.e. for 354,826 is 118

LCM of denominators i.e. for 46,700 is 16100.

Thus, GCF of Fractions is 118/16100.Finally, GCF of Fractions for 354/46, 826/700 is 118/16100.