How to Find GCF of 829/666, 420/642?

GCF of 829/666, 420/642

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 829/666, 420/642 i.e 1/71262 easily. The following is the detailed procedure to determine the greatest common factor of fractions 829/666, 420/642.

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 829/666,420/642?

Given fractions are 829/666,420/642

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 829/666,420/642, numerators are 829,420

Denominators are 666,642

The GCF of 829,420 is 1 .

LCM of 666,642 is 71262.

The greatest common factor of 829/666,420/642 = [GCF of 829,420]/[LCM of 666,642]= 1/71262

Therefore, the GCF of 829/666,420/642 is 1/71262.

Greatest Common Factor of 829,420

To find the highest common factor of 829,420, we have to find the factors of both numbers and list the highest common factor.

The factors of 829 are 1, 829

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The HCF of 829,420 is 1.

Lets's calculate GCF of 829,420

Greatest Common Factor (GCF) of 829,420 By Common Division

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

Greatest Common Factor of 829,420 By Matching Biggest Common Factor Method

Now, list down the factors of 829

1,829

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 829,420 . The biggest common factor number is the GCF number.
So the greatest common factor 829,420 is 1.

Lets's calculate LCM of 666,642

Lowest Common Multiple of 666,642 using Common Division

2	666, 642
3	333, 321
	111, 107

∴ So the LCM of the given numbers is 2 x 3 x 111 x 107 = 71262

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/71262

Therefore, the GCF of Fractions 829/666,420/642 is 1/71262

Least Common Multiple of 666,642 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 666,642 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(666,642) = 6

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

GCF(666,642) x common factors =6 x 1 = 6

LCM(666,642) = ( 666 × 642 ) / 6

LCM(666,642) = 427572 / 6

LCM(666,642) = 71262

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FAQs on GCF of Fractions of 829/666, 420/642

1. What is the HCF of 829,420?

The HCF of 829,420 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 829/666, 420/642?

Answer: GCF of Numerators as per given numbers 829/666, 420/642 is

GCF of Numerators i.e. for 829,420 is 1

LCM of denominators i.e. for 666,642 is 71262.

Thus, GCF of Fractions is 1/71262.Finally, GCF of Fractions for 829/666, 420/642 is 1/71262.