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GCF of 434/65, 557/659

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 434/65, 557/659 i.e 1/42835 easily. The following is the detailed procedure to determine the greatest common factor of fractions 434/65, 557/659.

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 434/65,557/659?

Given fractions are 434/65,557/659

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 434/65,557/659, numerators are 434,557

Denominators are 65,659

The GCF of 434,557 is 1 .

LCM of 65,659 is 42835.

The greatest common factor of 434/65,557/659 = [GCF of 434,557]/[LCM of 65,659]= 1/42835

Therefore, the GCF of 434/65,557/659 is 1/42835.

Greatest Common Factor of 434,557

To find the highest common factor of 434,557, we have to find the factors of both numbers and list the highest common factor.

The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434

The factors of 557 are 1, 557

The HCF of 434,557 is 1.

Lets's calculate GCF of 434,557

Greatest Common Factor (GCF) of 434,557 By Common Division

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

Greatest Common Factor of 434,557 By Matching Biggest Common Factor Method

Greatest Common Factor of 434,557 By Matching Biggest Common Factor Method

Now, list down the factors of 434

:

1,2,7,14,31,62,217,434

Now, list down the factors of 557

:

1,557

Greatest Common Factor

We found the factors 434,557 . The biggest common factor number is the GCF number.
So the greatest common factor 434,557 is 1.

Lets's calculate LCM of 65,659

Lowest Common Multiple of 65,659 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 42835

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42835

Therefore, the GCF of Fractions 434/65,557/659 is 1/42835

Least Common Multiple of 65,659 with GCF Formula

Least Common Multiple of 65,659 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 65,659 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,659) = 1

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

GCF(65,659) x common factors =1 x 1 = 1

LCM(65,659) = ( 65 × 659 ) / 1

LCM(65,659) = 42835 / 1

LCM(65,659) = 42835


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FAQs on GCF of Fractions of 434/65, 557/659

1. What is the HCF of 434,557?

The HCF of 434,557 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 434/65, 557/659?

Answer: GCF of Numerators as per given numbers 434/65, 557/659 is

GCF of Numerators i.e. for 434,557 is 1

LCM of denominators i.e. for 65,659 is 42835.

Thus, GCF of Fractions is 1/42835.Finally, GCF of Fractions for 434/65, 557/659 is 1/42835.