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GCF of 235/312, 709/704

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 235/312, 709/704 i.e 1/27456 easily. The following is the detailed procedure to determine the greatest common factor of fractions 235/312, 709/704.

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 235/312,709/704?

Given fractions are 235/312,709/704

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 235/312,709/704, numerators are 235,709

Denominators are 312,704

The GCF of 235,709 is 1 .

LCM of 312,704 is 27456.

The greatest common factor of 235/312,709/704 = [GCF of 235,709]/[LCM of 312,704]= 1/27456

Therefore, the GCF of 235/312,709/704 is 1/27456.

Greatest Common Factor of 235,709

To find the highest common factor of 235,709, we have to find the factors of both numbers and list the highest common factor.

The factors of 235 are 1, 5, 47, 235

The factors of 709 are 1, 709

The HCF of 235,709 is 1.

Lets's calculate GCF of 235,709

Greatest Common Factor (GCF) of 235,709 By Common Division

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

Greatest Common Factor of 235,709 By Matching Biggest Common Factor Method

Greatest Common Factor of 235,709 By Matching Biggest Common Factor Method

Now, list down the factors of 235

:

1,5,47,235

Now, list down the factors of 709

:

1,709

Greatest Common Factor

We found the factors 235,709 . The biggest common factor number is the GCF number.
So the greatest common factor 235,709 is 1.

Lets's calculate LCM of 312,704

Lowest Common Multiple of 312,704 using Common Division

2 312, 704
2 156, 352
2 78, 176
39, 88

∴ So the LCM of the given numbers is 2 x 2 x 2 x 39 x 88 = 27456

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27456

Therefore, the GCF of Fractions 235/312,709/704 is 1/27456

Least Common Multiple of 312,704 with GCF Formula

Least Common Multiple of 312,704 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 312,704 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(312,704) = 8

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

GCF(312,704) x common factors =8 x 1 = 8

LCM(312,704) = ( 312 × 704 ) / 8

LCM(312,704) = 219648 / 8

LCM(312,704) = 27456


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FAQs on GCF of Fractions of 235/312, 709/704

1. What is the HCF of 235,709?

The HCF of 235,709 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 235/312, 709/704?

Answer: GCF of Numerators as per given numbers 235/312, 709/704 is

GCF of Numerators i.e. for 235,709 is 1

LCM of denominators i.e. for 312,704 is 27456.

Thus, GCF of Fractions is 1/27456.Finally, GCF of Fractions for 235/312, 709/704 is 1/27456.