How to Find GCF of 1459/469, 8614/7322?

GCF of 1459/469, 8614/7322

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 1459/469, 8614/7322 i.e 1/490574 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1459/469, 8614/7322.

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 1459/469,8614/7322?

Given fractions are 1459/469,8614/7322

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 1459/469,8614/7322, numerators are 1459,8614

Denominators are 469,7322

The GCF of 1459,8614 is 1 .

LCM of 469,7322 is 490574.

The greatest common factor of 1459/469,8614/7322 = [GCF of 1459,8614]/[LCM of 469,7322]= 1/490574

Therefore, the GCF of 1459/469,8614/7322 is 1/490574.

Greatest Common Factor of 1459,8614

To find the highest common factor of 1459,8614, we have to find the factors of both numbers and list the highest common factor.

The factors of 1459 are 1, 1459

The factors of 8614 are 1, 2, 59, 73, 118, 146, 4307, 8614

The HCF of 1459,8614 is 1.

Lets's calculate GCF of 1459,8614

Greatest Common Factor (GCF) of 1459,8614 By Common Division

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

Greatest Common Factor of 1459,8614 By Matching Biggest Common Factor Method

Now, list down the factors of 1459

1,1459

Now, list down the factors of 8614

1,2,59,73,118,146,4307,8614

Greatest Common Factor

We found the factors 1459,8614 . The biggest common factor number is the GCF number.
So the greatest common factor 1459,8614 is 1.

Lets's calculate LCM of 469,7322

Lowest Common Multiple of 469,7322 using Common Division

7	469, 7322
	67, 1046

∴ So the LCM of the given numbers is 7 x 67 x 1046 = 490574

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/490574

Therefore, the GCF of Fractions 1459/469,8614/7322 is 1/490574

Least Common Multiple of 469,7322 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 469,7322 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(469,7322) = 7

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

GCF(469,7322) x common factors =7 x 1 = 7

LCM(469,7322) = ( 469 × 7322 ) / 7

LCM(469,7322) = 3434018 / 7

LCM(469,7322) = 490574

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FAQs on GCF of Fractions of 1459/469, 8614/7322

1. What is the HCF of 1459,8614?

The HCF of 1459,8614 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 1459/469, 8614/7322?

Answer: GCF of Numerators as per given numbers 1459/469, 8614/7322 is

GCF of Numerators i.e. for 1459,8614 is 1

LCM of denominators i.e. for 469,7322 is 490574.

Thus, GCF of Fractions is 1/490574.Finally, GCF of Fractions for 1459/469, 8614/7322 is 1/490574.