How to Find GCF of 992/747, 288/766?

GCF of 992/747, 288/766

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 992/747, 288/766 i.e 32/572202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 992/747, 288/766.

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 992/747,288/766?

Given fractions are 992/747,288/766

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 992/747,288/766, numerators are 992,288

Denominators are 747,766

The GCF of 992,288 is 32 .

LCM of 747,766 is 572202.

The greatest common factor of 992/747,288/766 = [GCF of 992,288]/[LCM of 747,766]= 32/572202

Therefore, the GCF of 992/747,288/766 is 32/572202.

Greatest Common Factor of 992,288

To find the highest common factor of 992,288, we have to find the factors of both numbers and list the highest common factor.

The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

The HCF of 992,288 is 32.

Lets's calculate GCF of 992,288

Greatest Common Factor (GCF) of 992,288 By Common Division

2	992, 288
2	496, 144
2	248, 72
2	124, 36
2	62, 18
	31, 9

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 992,288 By Matching Biggest Common Factor Method

Now, list down the factors of 992

1,2,4,8,16,31,32,62,124,248,496,992

Now, list down the factors of 288

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Greatest Common Factor

We found the factors 992,288 . The biggest common factor number is the GCF number.
So the greatest common factor 992,288 is 32.

Lets's calculate LCM of 747,766

Lowest Common Multiple of 747,766 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 572202

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/572202

Therefore, the GCF of Fractions 992/747,288/766 is 32/572202

Least Common Multiple of 747,766 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 747,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(747,766) = 1

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

GCF(747,766) x common factors =1 x 1 = 1

LCM(747,766) = ( 747 × 766 ) / 1

LCM(747,766) = 572202 / 1

LCM(747,766) = 572202

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FAQs on GCF of Fractions of 992/747, 288/766

1. What is the HCF of 992,288?

The HCF of 992,288 is 32

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 992/747, 288/766?

Answer: GCF of Numerators as per given numbers 992/747, 288/766 is

GCF of Numerators i.e. for 992,288 is 32

LCM of denominators i.e. for 747,766 is 572202.

Thus, GCF of Fractions is 32/572202.Finally, GCF of Fractions for 992/747, 288/766 is 32/572202.