How to Find GCF of 421/692, 5698/892?

GCF of 421/692, 5698/892

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 421/692, 5698/892 i.e 1/154316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 421/692, 5698/892.

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 421/692,5698/892?

Given fractions are 421/692,5698/892

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 421/692,5698/892, numerators are 421,5698

Denominators are 692,892

The GCF of 421,5698 is 1 .

LCM of 692,892 is 154316.

The greatest common factor of 421/692,5698/892 = [GCF of 421,5698]/[LCM of 692,892]= 1/154316

Therefore, the GCF of 421/692,5698/892 is 1/154316.

Greatest Common Factor of 421,5698

To find the highest common factor of 421,5698, we have to find the factors of both numbers and list the highest common factor.

The factors of 421 are 1, 421

The factors of 5698 are 1, 2, 7, 11, 14, 22, 37, 74, 77, 154, 259, 407, 518, 814, 2849, 5698

The HCF of 421,5698 is 1.

Lets's calculate GCF of 421,5698

Greatest Common Factor (GCF) of 421,5698 By Common Division

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

Greatest Common Factor of 421,5698 By Matching Biggest Common Factor Method

Now, list down the factors of 421

1,421

Now, list down the factors of 5698

1,2,7,11,14,22,37,74,77,154,259,407,518,814,2849,5698

Greatest Common Factor

We found the factors 421,5698 . The biggest common factor number is the GCF number.
So the greatest common factor 421,5698 is 1.

Lets's calculate LCM of 692,892

Lowest Common Multiple of 692,892 using Common Division

2	692, 892
2	346, 446
	173, 223

∴ So the LCM of the given numbers is 2 x 2 x 173 x 223 = 154316

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/154316

Therefore, the GCF of Fractions 421/692,5698/892 is 1/154316

Least Common Multiple of 692,892 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 692,892 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(692,892) = 4

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

GCF(692,892) x common factors =4 x 1 = 4

LCM(692,892) = ( 692 × 892 ) / 4

LCM(692,892) = 617264 / 4

LCM(692,892) = 154316

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FAQs on GCF of Fractions of 421/692, 5698/892

1. What is the HCF of 421,5698?

The HCF of 421,5698 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 421/692, 5698/892?

Answer: GCF of Numerators as per given numbers 421/692, 5698/892 is

GCF of Numerators i.e. for 421,5698 is 1

LCM of denominators i.e. for 692,892 is 154316.

Thus, GCF of Fractions is 1/154316.Finally, GCF of Fractions for 421/692, 5698/892 is 1/154316.