How to Find GCF of 1326/120, 2567/1780?

GCF of 1326/120, 2567/1780

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 1326/120, 2567/1780 i.e 17/10680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1326/120, 2567/1780.

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 1326/120,2567/1780?

Given fractions are 1326/120,2567/1780

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 1326/120,2567/1780, numerators are 1326,2567

Denominators are 120,1780

The GCF of 1326,2567 is 17 .

LCM of 120,1780 is 10680.

The greatest common factor of 1326/120,2567/1780 = [GCF of 1326,2567]/[LCM of 120,1780]= 17/10680

Therefore, the GCF of 1326/120,2567/1780 is 17/10680.

Greatest Common Factor of 1326,2567

To find the highest common factor of 1326,2567, we have to find the factors of both numbers and list the highest common factor.

The factors of 1326 are 1, 2, 3, 6, 13, 17, 26, 34, 39, 51, 78, 102, 221, 442, 663, 1326

The factors of 2567 are 1, 17, 151, 2567

The HCF of 1326,2567 is 17.

Lets's calculate GCF of 1326,2567

Greatest Common Factor (GCF) of 1326,2567 By Common Division

17	1326, 2567
	78, 151

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 1326,2567 By Matching Biggest Common Factor Method

Now, list down the factors of 1326

1,2,3,6,13,17,26,34,39,51,78,102,221,442,663,1326

Now, list down the factors of 2567

1,17,151,2567

Greatest Common Factor

We found the factors 1326,2567 . The biggest common factor number is the GCF number.
So the greatest common factor 1326,2567 is 17.

Lets's calculate LCM of 120,1780

Lowest Common Multiple of 120,1780 using Common Division

2	120, 1780
2	60, 890
5	30, 445
	6, 89

∴ So the LCM of the given numbers is 2 x 2 x 5 x 6 x 89 = 10680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/10680

Therefore, the GCF of Fractions 1326/120,2567/1780 is 17/10680

Least Common Multiple of 120,1780 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 120,1780 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(120,1780) = 20

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

GCF(120,1780) x common factors =20 x 1 = 20

LCM(120,1780) = ( 120 × 1780 ) / 20

LCM(120,1780) = 213600 / 20

LCM(120,1780) = 10680

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FAQs on GCF of Fractions of 1326/120, 2567/1780

1. What is the HCF of 1326,2567?

The HCF of 1326,2567 is 17

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 1326/120, 2567/1780?

Answer: GCF of Numerators as per given numbers 1326/120, 2567/1780 is

GCF of Numerators i.e. for 1326,2567 is 17

LCM of denominators i.e. for 120,1780 is 10680.

Thus, GCF of Fractions is 17/10680.Finally, GCF of Fractions for 1326/120, 2567/1780 is 17/10680.