How to Find GCF of 1721/218, 4536/9760?

GCF of 1721/218, 4536/9760

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 1721/218, 4536/9760 i.e 1/1063840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1721/218, 4536/9760.

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 1721/218,4536/9760?

Given fractions are 1721/218,4536/9760

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 1721/218,4536/9760, numerators are 1721,4536

Denominators are 218,9760

The GCF of 1721,4536 is 1 .

LCM of 218,9760 is 1063840.

The greatest common factor of 1721/218,4536/9760 = [GCF of 1721,4536]/[LCM of 218,9760]= 1/1063840

Therefore, the GCF of 1721/218,4536/9760 is 1/1063840.

Greatest Common Factor of 1721,4536

To find the highest common factor of 1721,4536, we have to find the factors of both numbers and list the highest common factor.

The factors of 1721 are 1, 1721

The factors of 4536 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 81, 84, 108, 126, 162, 168, 189, 216, 252, 324, 378, 504, 567, 648, 756, 1134, 1512, 2268, 4536

The HCF of 1721,4536 is 1.

Lets's calculate GCF of 1721,4536

Greatest Common Factor (GCF) of 1721,4536 By Common Division

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

Greatest Common Factor of 1721,4536 By Matching Biggest Common Factor Method

Now, list down the factors of 1721

1,1721

Now, list down the factors of 4536

1,2,3,4,6,7,8,9,12,14,18,21,24,27,28,36,42,54,56,63,72,81,84,108,126,162,168,189,216,252,324,378,504,567,648,756,1134,1512,2268,4536

Greatest Common Factor

We found the factors 1721,4536 . The biggest common factor number is the GCF number.
So the greatest common factor 1721,4536 is 1.

Lets's calculate LCM of 218,9760

Lowest Common Multiple of 218,9760 using Common Division

2	218, 9760
	109, 4880

∴ So the LCM of the given numbers is 2 x 109 x 4880 = 1063840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1063840

Therefore, the GCF of Fractions 1721/218,4536/9760 is 1/1063840

Least Common Multiple of 218,9760 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 218,9760 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(218,9760) = 2

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

GCF(218,9760) x common factors =2 x 1 = 2

LCM(218,9760) = ( 218 × 9760 ) / 2

LCM(218,9760) = 2127680 / 2

LCM(218,9760) = 1063840

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FAQs on GCF of Fractions of 1721/218, 4536/9760

1. What is the HCF of 1721,4536?

The HCF of 1721,4536 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 1721/218, 4536/9760?

Answer: GCF of Numerators as per given numbers 1721/218, 4536/9760 is

GCF of Numerators i.e. for 1721,4536 is 1

LCM of denominators i.e. for 218,9760 is 1063840.

Thus, GCF of Fractions is 1/1063840.Finally, GCF of Fractions for 1721/218, 4536/9760 is 1/1063840.