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GCF of 705/314, 7243/120

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 705/314, 7243/120 i.e 1/18840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/314, 7243/120.

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 705/314,7243/120?

Given fractions are 705/314,7243/120

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 705/314,7243/120, numerators are 705,7243

Denominators are 314,120

The GCF of 705,7243 is 1 .

LCM of 314,120 is 18840.

The greatest common factor of 705/314,7243/120 = [GCF of 705,7243]/[LCM of 314,120]= 1/18840

Therefore, the GCF of 705/314,7243/120 is 1/18840.

Greatest Common Factor of 705,7243

To find the highest common factor of 705,7243, we have to find the factors of both numbers and list the highest common factor.

The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705

The factors of 7243 are 1, 7243

The HCF of 705,7243 is 1.

Lets's calculate GCF of 705,7243

Greatest Common Factor (GCF) of 705,7243 By Common Division

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

Greatest Common Factor of 705,7243 By Matching Biggest Common Factor Method

Greatest Common Factor of 705,7243 By Matching Biggest Common Factor Method

Now, list down the factors of 705

:

1,3,5,15,47,141,235,705

Now, list down the factors of 7243

:

1,7243

Greatest Common Factor

We found the factors 705,7243 . The biggest common factor number is the GCF number.
So the greatest common factor 705,7243 is 1.

Lets's calculate LCM of 314,120

Lowest Common Multiple of 314,120 using Common Division

2 314, 120
157, 60

∴ So the LCM of the given numbers is 2 x 157 x 60 = 18840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18840

Therefore, the GCF of Fractions 705/314,7243/120 is 1/18840

Least Common Multiple of 314,120 with GCF Formula

Least Common Multiple of 314,120 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 314,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,120) = 2

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

GCF(314,120) x common factors =2 x 1 = 2

LCM(314,120) = ( 314 × 120 ) / 2

LCM(314,120) = 37680 / 2

LCM(314,120) = 18840


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FAQs on GCF of Fractions of 705/314, 7243/120

1. What is the HCF of 705,7243?

The HCF of 705,7243 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 705/314, 7243/120?

Answer: GCF of Numerators as per given numbers 705/314, 7243/120 is

GCF of Numerators i.e. for 705,7243 is 1

LCM of denominators i.e. for 314,120 is 18840.

Thus, GCF of Fractions is 1/18840.Finally, GCF of Fractions for 705/314, 7243/120 is 1/18840.