How to Find GCF of 912/100, 828/320?

GCF of 912/100, 828/320

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 912/100, 828/320 i.e 12/1600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 912/100, 828/320.

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 912/100,828/320?

Given fractions are 912/100,828/320

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 912/100,828/320, numerators are 912,828

Denominators are 100,320

The GCF of 912,828 is 12 .

LCM of 100,320 is 1600.

The greatest common factor of 912/100,828/320 = [GCF of 912,828]/[LCM of 100,320]= 12/1600

Therefore, the GCF of 912/100,828/320 is 12/1600.

Greatest Common Factor of 912,828

To find the highest common factor of 912,828, we have to find the factors of both numbers and list the highest common factor.

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 factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828

The HCF of 912,828 is 12.

Lets's calculate GCF of 912,828

Greatest Common Factor (GCF) of 912,828 By Common Division

2	912, 828
2	456, 414
3	228, 207
	76, 69

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 912,828 By Matching Biggest Common Factor Method

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

Now, list down the factors of 828

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Greatest Common Factor

We found the factors 912,828 . The biggest common factor number is the GCF number.
So the greatest common factor 912,828 is 12.

Lets's calculate LCM of 100,320

Lowest Common Multiple of 100,320 using Common Division

2	100, 320
2	50, 160
5	25, 80
	5, 16

∴ So the LCM of the given numbers is 2 x 2 x 5 x 5 x 16 = 1600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/1600

Therefore, the GCF of Fractions 912/100,828/320 is 12/1600

Least Common Multiple of 100,320 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 100,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(100,320) = 20

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

GCF(100,320) x common factors =20 x 1 = 20

LCM(100,320) = ( 100 × 320 ) / 20

LCM(100,320) = 32000 / 20

LCM(100,320) = 1600

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FAQs on GCF of Fractions of 912/100, 828/320

1. What is the HCF of 912,828?

The HCF of 912,828 is 12

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 912/100, 828/320?

Answer: GCF of Numerators as per given numbers 912/100, 828/320 is

GCF of Numerators i.e. for 912,828 is 12

LCM of denominators i.e. for 100,320 is 1600.

Thus, GCF of Fractions is 12/1600.Finally, GCF of Fractions for 912/100, 828/320 is 12/1600.