How to Find GCF of 21/759, 90/762, 323/782?

GCF of 21/759, 90/762, 323/782

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 21/759, 90/762, 323/782 i.e 1/3277362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/759, 90/762, 323/782.

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 21/759,90/762,323/782?

Given fractions are 21/759,90/762,323/782

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 21/759,90/762,323/782, numerators are 21,90,323

Denominators are 759,762,782

The GCF of 21,90,323 is 1 .

LCM of 759,762,782 is 3277362.

The greatest common factor of 21/759,90/762,323/782 = [GCF of 21,90,323]/[LCM of 759,762,782]= 1/3277362

Therefore, the GCF of 21/759,90/762,323/782 is 1/3277362.

Greatest Common Factor of 21,90,323

To find the highest common factor of 21,90,323, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The factors of 323 are 1, 17, 19, 323

The HCF of 21,90,323 is 1.

Lets's calculate GCF of 21,90,323

Greatest Common Factor (GCF) of 21,90,323 By Common Division

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

Greatest Common Factor of 21,90,323 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 90

1,2,3,5,6,9,10,15,18,30,45,90

Now, list down the factors of 323

1,17,19,323

Greatest Common Factor

We found the factors 21,90,323 . The biggest common factor number is the GCF number.
So the greatest common factor 21,90,323 is 1.

Lets's calculate LCM of 759,762,782

Lowest Common Multiple of 759,762,782 using Common Division

2	759, 762, 782
3	759, 381, 391
23	253, 127, 391
	11, 127, 17

∴ So the LCM of the given numbers is 2 x 3 x 23 x 11 x 127 x 17 = 3277362

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3277362

Therefore, the GCF of Fractions 21/759,90/762,323/782 is 1/3277362

Least Common Multiple of 759,762,782 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 759,762,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(759,762,782) = 1

common factors(in case of two or more numbers have common factors) = 138

GCF(759,762,782) x common factors =1 x 138 = 138

LCM(759,762,782) = ( 759 × 762 × 782 ) / 138

LCM(759,762,782) = 452275956 / 138

LCM(759,762,782) = 3277362

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 21/759, 90/762, 323/782

1. What is the HCF of 21,90,323?

The HCF of 21,90,323 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 21/759, 90/762, 323/782?

Answer: GCF of Numerators as per given numbers 21/759, 90/762, 323/782 is

GCF of Numerators i.e. for 21,90,323 is 1

LCM of denominators i.e. for 759,762,782 is 3277362.

Thus, GCF of Fractions is 1/3277362.Finally, GCF of Fractions for 21/759, 90/762, 323/782 is 1/3277362.