How to Find GCF of 7216/744, 1148/1781?

GCF of 7216/744, 1148/1781

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 7216/744, 1148/1781 i.e 164/1325064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7216/744, 1148/1781.

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 7216/744,1148/1781?

Given fractions are 7216/744,1148/1781

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 7216/744,1148/1781, numerators are 7216,1148

Denominators are 744,1781

The GCF of 7216,1148 is 164 .

LCM of 744,1781 is 1325064.

The greatest common factor of 7216/744,1148/1781 = [GCF of 7216,1148]/[LCM of 744,1781]= 164/1325064

Therefore, the GCF of 7216/744,1148/1781 is 164/1325064.

Greatest Common Factor of 7216,1148

To find the highest common factor of 7216,1148, we have to find the factors of both numbers and list the highest common factor.

The factors of 7216 are 1, 2, 4, 8, 11, 16, 22, 41, 44, 82, 88, 164, 176, 328, 451, 656, 902, 1804, 3608, 7216

The factors of 1148 are 1, 2, 4, 7, 14, 28, 41, 82, 164, 287, 574, 1148

The HCF of 7216,1148 is 164.

Lets's calculate GCF of 7216,1148

Greatest Common Factor (GCF) of 7216,1148 By Common Division

2	7216, 1148
2	3608, 574
41	1804, 287
	44, 7

∴ So the GCF of the given numbers is 2 x 2 x 41 = 164

Greatest Common Factor of 7216,1148 By Matching Biggest Common Factor Method

Now, list down the factors of 7216

1,2,4,8,11,16,22,41,44,82,88,164,176,328,451,656,902,1804,3608,7216

Now, list down the factors of 1148

1,2,4,7,14,28,41,82,164,287,574,1148

Greatest Common Factor

We found the factors 7216,1148 . The biggest common factor number is the GCF number.
So the greatest common factor 7216,1148 is 164.

Lets's calculate LCM of 744,1781

Lowest Common Multiple of 744,1781 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1325064

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 164/1325064

Therefore, the GCF of Fractions 7216/744,1148/1781 is 164/1325064

Least Common Multiple of 744,1781 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 744,1781 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(744,1781) = 1

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

GCF(744,1781) x common factors =1 x 1 = 1

LCM(744,1781) = ( 744 × 1781 ) / 1

LCM(744,1781) = 1325064 / 1

LCM(744,1781) = 1325064

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FAQs on GCF of Fractions of 7216/744, 1148/1781

1. What is the HCF of 7216,1148?

The HCF of 7216,1148 is 164

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 7216/744, 1148/1781?

Answer: GCF of Numerators as per given numbers 7216/744, 1148/1781 is

GCF of Numerators i.e. for 7216,1148 is 164

LCM of denominators i.e. for 744,1781 is 1325064.

Thus, GCF of Fractions is 164/1325064.Finally, GCF of Fractions for 7216/744, 1148/1781 is 164/1325064.