How to Find GCF of 1460/209, 6123/540?

GCF of 1460/209, 6123/540

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 1460/209, 6123/540 i.e 1/112860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1460/209, 6123/540.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 1460/209,6123/540?

Given fractions are 1460/209,6123/540

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 1460/209,6123/540, numerators are 1460,6123

Denominators are 209,540

The GCF of 1460,6123 is 1 .

LCM of 209,540 is 112860.

The greatest common factor of 1460/209,6123/540 = [GCF of 1460,6123]/[LCM of 209,540]= 1/112860

Therefore, the GCF of 1460/209,6123/540 is 1/112860.

Greatest Common Factor of 1460,6123

To find the highest common factor of 1460,6123, we have to find the factors of both numbers and list the highest common factor.

The factors of 1460 are 1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730, 1460

The factors of 6123 are 1, 3, 13, 39, 157, 471, 2041, 6123

The HCF of 1460,6123 is 1.

Lets's calculate GCF of 1460,6123

Greatest Common Factor (GCF) of 1460,6123 By Common Division

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

Greatest Common Factor of 1460,6123 By Matching Biggest Common Factor Method

Now, list down the factors of 1460

1,2,4,5,10,20,73,146,292,365,730,1460

Now, list down the factors of 6123

1,3,13,39,157,471,2041,6123

Greatest Common Factor

We found the factors 1460,6123 . The biggest common factor number is the GCF number.
So the greatest common factor 1460,6123 is 1.

Lets's calculate LCM of 209,540

Lowest Common Multiple of 209,540 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 112860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/112860

Therefore, the GCF of Fractions 1460/209,6123/540 is 1/112860

Least Common Multiple of 209,540 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 209,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(209,540) = 1

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

GCF(209,540) x common factors =1 x 1 = 1

LCM(209,540) = ( 209 × 540 ) / 1

LCM(209,540) = 112860 / 1

LCM(209,540) = 112860

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FAQs on GCF of Fractions of 1460/209, 6123/540

1. What is the HCF of 1460,6123?

The HCF of 1460,6123 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 1460/209, 6123/540?

Answer: GCF of Numerators as per given numbers 1460/209, 6123/540 is

GCF of Numerators i.e. for 1460,6123 is 1

LCM of denominators i.e. for 209,540 is 112860.

Thus, GCF of Fractions is 1/112860.Finally, GCF of Fractions for 1460/209, 6123/540 is 1/112860.