How to Find GCF of 67/260, 7657/1500?

GCF of 67/260, 7657/1500

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 67/260, 7657/1500 i.e 1/19500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/260, 7657/1500.

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 67/260,7657/1500?

Given fractions are 67/260,7657/1500

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 67/260,7657/1500, numerators are 67,7657

Denominators are 260,1500

The GCF of 67,7657 is 1 .

LCM of 260,1500 is 19500.

The greatest common factor of 67/260,7657/1500 = [GCF of 67,7657]/[LCM of 260,1500]= 1/19500

Therefore, the GCF of 67/260,7657/1500 is 1/19500.

Greatest Common Factor of 67,7657

To find the highest common factor of 67,7657, we have to find the factors of both numbers and list the highest common factor.

The factors of 67 are 1, 67

The factors of 7657 are 1, 13, 19, 31, 247, 403, 589, 7657

The HCF of 67,7657 is 1.

Lets's calculate GCF of 67,7657

Greatest Common Factor (GCF) of 67,7657 By Common Division

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

Greatest Common Factor of 67,7657 By Matching Biggest Common Factor Method

Now, list down the factors of 67

1,67

Now, list down the factors of 7657

1,13,19,31,247,403,589,7657

Greatest Common Factor

We found the factors 67,7657 . The biggest common factor number is the GCF number.
So the greatest common factor 67,7657 is 1.

Lets's calculate LCM of 260,1500

Lowest Common Multiple of 260,1500 using Common Division

2	260, 1500
2	130, 750
5	65, 375
	13, 75

∴ So the LCM of the given numbers is 2 x 2 x 5 x 13 x 75 = 19500

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19500

Therefore, the GCF of Fractions 67/260,7657/1500 is 1/19500

Least Common Multiple of 260,1500 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 260,1500 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(260,1500) = 20

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

GCF(260,1500) x common factors =20 x 1 = 20

LCM(260,1500) = ( 260 × 1500 ) / 20

LCM(260,1500) = 390000 / 20

LCM(260,1500) = 19500

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FAQs on GCF of Fractions of 67/260, 7657/1500

1. What is the HCF of 67,7657?

The HCF of 67,7657 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 67/260, 7657/1500?

Answer: GCF of Numerators as per given numbers 67/260, 7657/1500 is

GCF of Numerators i.e. for 67,7657 is 1

LCM of denominators i.e. for 260,1500 is 19500.

Thus, GCF of Fractions is 1/19500.Finally, GCF of Fractions for 67/260, 7657/1500 is 1/19500.