How to Find GCF of 462/508, 9649/448?

GCF of 462/508, 9649/448

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 462/508, 9649/448 i.e 1/56896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 462/508, 9649/448.

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 462/508,9649/448?

Given fractions are 462/508,9649/448

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 462/508,9649/448, numerators are 462,9649

Denominators are 508,448

The GCF of 462,9649 is 1 .

LCM of 508,448 is 56896.

The greatest common factor of 462/508,9649/448 = [GCF of 462,9649]/[LCM of 508,448]= 1/56896

Therefore, the GCF of 462/508,9649/448 is 1/56896.

Greatest Common Factor of 462,9649

To find the highest common factor of 462,9649, we have to find the factors of both numbers and list the highest common factor.

The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

The factors of 9649 are 1, 9649

The HCF of 462,9649 is 1.

Lets's calculate GCF of 462,9649

Greatest Common Factor (GCF) of 462,9649 By Common Division

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

Greatest Common Factor of 462,9649 By Matching Biggest Common Factor Method

Now, list down the factors of 462

1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462

Now, list down the factors of 9649

1,9649

Greatest Common Factor

We found the factors 462,9649 . The biggest common factor number is the GCF number.
So the greatest common factor 462,9649 is 1.

Lets's calculate LCM of 508,448

Lowest Common Multiple of 508,448 using Common Division

2	508, 448
2	254, 224
	127, 112

∴ So the LCM of the given numbers is 2 x 2 x 127 x 112 = 56896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56896

Therefore, the GCF of Fractions 462/508,9649/448 is 1/56896

Least Common Multiple of 508,448 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 508,448 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(508,448) = 4

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

GCF(508,448) x common factors =4 x 1 = 4

LCM(508,448) = ( 508 × 448 ) / 4

LCM(508,448) = 227584 / 4

LCM(508,448) = 56896

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FAQs on GCF of Fractions of 462/508, 9649/448

1. What is the HCF of 462,9649?

The HCF of 462,9649 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 462/508, 9649/448?

Answer: GCF of Numerators as per given numbers 462/508, 9649/448 is

GCF of Numerators i.e. for 462,9649 is 1

LCM of denominators i.e. for 508,448 is 56896.

Thus, GCF of Fractions is 1/56896.Finally, GCF of Fractions for 462/508, 9649/448 is 1/56896.