How to Find GCF of 107/598, 590/689?

GCF of 107/598, 590/689

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 107/598, 590/689 i.e 1/31694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 107/598, 590/689.

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 107/598,590/689?

Given fractions are 107/598,590/689

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 107/598,590/689, numerators are 107,590

Denominators are 598,689

The GCF of 107,590 is 1 .

LCM of 598,689 is 31694.

The greatest common factor of 107/598,590/689 = [GCF of 107,590]/[LCM of 598,689]= 1/31694

Therefore, the GCF of 107/598,590/689 is 1/31694.

Greatest Common Factor of 107,590

To find the highest common factor of 107,590, we have to find the factors of both numbers and list the highest common factor.

The factors of 107 are 1, 107

The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590

The HCF of 107,590 is 1.

Lets's calculate GCF of 107,590

Greatest Common Factor (GCF) of 107,590 By Common Division

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

Greatest Common Factor of 107,590 By Matching Biggest Common Factor Method

Now, list down the factors of 107

1,107

Now, list down the factors of 590

1,2,5,10,59,118,295,590

Greatest Common Factor

We found the factors 107,590 . The biggest common factor number is the GCF number.
So the greatest common factor 107,590 is 1.

Lets's calculate LCM of 598,689

Lowest Common Multiple of 598,689 using Common Division

13	598, 689
	46, 53

∴ So the LCM of the given numbers is 13 x 46 x 53 = 31694

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31694

Therefore, the GCF of Fractions 107/598,590/689 is 1/31694

Least Common Multiple of 598,689 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 598,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(598,689) = 13

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

GCF(598,689) x common factors =13 x 1 = 13

LCM(598,689) = ( 598 × 689 ) / 13

LCM(598,689) = 412022 / 13

LCM(598,689) = 31694

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FAQs on GCF of Fractions of 107/598, 590/689

1. What is the HCF of 107,590?

The HCF of 107,590 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 107/598, 590/689?

Answer: GCF of Numerators as per given numbers 107/598, 590/689 is

GCF of Numerators i.e. for 107,590 is 1

LCM of denominators i.e. for 598,689 is 31694.

Thus, GCF of Fractions is 1/31694.Finally, GCF of Fractions for 107/598, 590/689 is 1/31694.