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GCF of 290/509, 140/746

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 290/509, 140/746 i.e 10/379714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 290/509, 140/746.

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 290/509,140/746?

Given fractions are 290/509,140/746

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 290/509,140/746, numerators are 290,140

Denominators are 509,746

The GCF of 290,140 is 10 .

LCM of 509,746 is 379714.

The greatest common factor of 290/509,140/746 = [GCF of 290,140]/[LCM of 509,746]= 10/379714

Therefore, the GCF of 290/509,140/746 is 10/379714.

Greatest Common Factor of 290,140

To find the highest common factor of 290,140, we have to find the factors of both numbers and list the highest common factor.

The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290

The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

The HCF of 290,140 is 10.

Lets's calculate GCF of 290,140

Greatest Common Factor (GCF) of 290,140 By Common Division

2 290, 140
5 145, 70
29, 14

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 290,140 By Matching Biggest Common Factor Method

Greatest Common Factor of 290,140 By Matching Biggest Common Factor Method

Now, list down the factors of 290

:

1,2,5,10,29,58,145,290

Now, list down the factors of 140

:

1,2,4,5,7,10,14,20,28,35,70,140

Greatest Common Factor

We found the factors 290,140 . The biggest common factor number is the GCF number.
So the greatest common factor 290,140 is 10.

Lets's calculate LCM of 509,746

Lowest Common Multiple of 509,746 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 379714

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/379714

Therefore, the GCF of Fractions 290/509,140/746 is 10/379714

Least Common Multiple of 509,746 with GCF Formula

Least Common Multiple of 509,746 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 509,746 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(509,746) = 1

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

GCF(509,746) x common factors =1 x 1 = 1

LCM(509,746) = ( 509 × 746 ) / 1

LCM(509,746) = 379714 / 1

LCM(509,746) = 379714


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 290/509, 140/746

1. What is the HCF of 290,140?

The HCF of 290,140 is 10

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 290/509, 140/746?

Answer: GCF of Numerators as per given numbers 290/509, 140/746 is

GCF of Numerators i.e. for 290,140 is 10

LCM of denominators i.e. for 509,746 is 379714.

Thus, GCF of Fractions is 10/379714.Finally, GCF of Fractions for 290/509, 140/746 is 10/379714.