How to Find GCF of 565/896, 702/224?

GCF of 565/896, 702/224

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 565/896, 702/224 i.e 1/896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 565/896, 702/224.

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 565/896,702/224?

Given fractions are 565/896,702/224

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 565/896,702/224, numerators are 565,702

Denominators are 896,224

The GCF of 565,702 is 1 .

LCM of 896,224 is 896.

The greatest common factor of 565/896,702/224 = [GCF of 565,702]/[LCM of 896,224]= 1/896

Therefore, the GCF of 565/896,702/224 is 1/896.

Greatest Common Factor of 565,702

To find the highest common factor of 565,702, we have to find the factors of both numbers and list the highest common factor.

The factors of 565 are 1, 5, 113, 565

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

The HCF of 565,702 is 1.

Lets's calculate GCF of 565,702

Greatest Common Factor (GCF) of 565,702 By Common Division

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

Greatest Common Factor of 565,702 By Matching Biggest Common Factor Method

Now, list down the factors of 565

1,5,113,565

Now, list down the factors of 702

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Greatest Common Factor

We found the factors 565,702 . The biggest common factor number is the GCF number.
So the greatest common factor 565,702 is 1.

Lets's calculate LCM of 896,224

Lowest Common Multiple of 896,224 using Common Division

2	896, 224
2	448, 112
2	224, 56
2	112, 28
2	56, 14
7	28, 7
	4, 1

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 7 x 4 x 1 = 896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/896

Therefore, the GCF of Fractions 565/896,702/224 is 1/896

Least Common Multiple of 896,224 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 896,224 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(896,224) = 224

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

GCF(896,224) x common factors =224 x 1 = 224

LCM(896,224) = ( 896 × 224 ) / 224

LCM(896,224) = 200704 / 224

LCM(896,224) = 896

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FAQs on GCF of Fractions of 565/896, 702/224

1. What is the HCF of 565,702?

The HCF of 565,702 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 565/896, 702/224?

Answer: GCF of Numerators as per given numbers 565/896, 702/224 is

GCF of Numerators i.e. for 565,702 is 1

LCM of denominators i.e. for 896,224 is 896.

Thus, GCF of Fractions is 1/896.Finally, GCF of Fractions for 565/896, 702/224 is 1/896.