How to Find GCF of 512/22, 912/6415?

GCF of 512/22, 912/6415

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 512/22, 912/6415 i.e 16/141130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/22, 912/6415.

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 512/22,912/6415?

Given fractions are 512/22,912/6415

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 512/22,912/6415, numerators are 512,912

Denominators are 22,6415

The GCF of 512,912 is 16 .

LCM of 22,6415 is 141130.

The greatest common factor of 512/22,912/6415 = [GCF of 512,912]/[LCM of 22,6415]= 16/141130

Therefore, the GCF of 512/22,912/6415 is 16/141130.

Greatest Common Factor of 512,912

To find the highest common factor of 512,912, we have to find the factors of both numbers and list the highest common factor.

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The factors of 912 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912

The HCF of 512,912 is 16.

Lets's calculate GCF of 512,912

Greatest Common Factor (GCF) of 512,912 By Common Division

2	512, 912
2	256, 456
2	128, 228
2	64, 114
	32, 57

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 512,912 By Matching Biggest Common Factor Method

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Now, list down the factors of 912

1,2,3,4,6,8,12,16,19,24,38,48,57,76,114,152,228,304,456,912

Greatest Common Factor

We found the factors 512,912 . The biggest common factor number is the GCF number.
So the greatest common factor 512,912 is 16.

Lets's calculate LCM of 22,6415

Lowest Common Multiple of 22,6415 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 141130

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/141130

Therefore, the GCF of Fractions 512/22,912/6415 is 16/141130

Least Common Multiple of 22,6415 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 22,6415 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,6415) = 1

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

GCF(22,6415) x common factors =1 x 1 = 1

LCM(22,6415) = ( 22 × 6415 ) / 1

LCM(22,6415) = 141130 / 1

LCM(22,6415) = 141130

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FAQs on GCF of Fractions of 512/22, 912/6415

1. What is the HCF of 512,912?

The HCF of 512,912 is 16

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 512/22, 912/6415?

Answer: GCF of Numerators as per given numbers 512/22, 912/6415 is

GCF of Numerators i.e. for 512,912 is 16

LCM of denominators i.e. for 22,6415 is 141130.

Thus, GCF of Fractions is 16/141130.Finally, GCF of Fractions for 512/22, 912/6415 is 16/141130.