How to Find GCF of 1582/254, 5890/7601?

GCF of 1582/254, 5890/7601

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 1582/254, 5890/7601 i.e 2/1930654 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1582/254, 5890/7601.

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 1582/254,5890/7601?

Given fractions are 1582/254,5890/7601

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 1582/254,5890/7601, numerators are 1582,5890

Denominators are 254,7601

The GCF of 1582,5890 is 2 .

LCM of 254,7601 is 1930654.

The greatest common factor of 1582/254,5890/7601 = [GCF of 1582,5890]/[LCM of 254,7601]= 2/1930654

Therefore, the GCF of 1582/254,5890/7601 is 2/1930654.

Greatest Common Factor of 1582,5890

To find the highest common factor of 1582,5890, we have to find the factors of both numbers and list the highest common factor.

The factors of 1582 are 1, 2, 7, 14, 113, 226, 791, 1582

The factors of 5890 are 1, 2, 5, 10, 19, 31, 38, 62, 95, 155, 190, 310, 589, 1178, 2945, 5890

The HCF of 1582,5890 is 2.

Lets's calculate GCF of 1582,5890

Greatest Common Factor (GCF) of 1582,5890 By Common Division

2	1582, 5890
	791, 2945

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

Greatest Common Factor of 1582,5890 By Matching Biggest Common Factor Method

Now, list down the factors of 1582

1,2,7,14,113,226,791,1582

Now, list down the factors of 5890

1,2,5,10,19,31,38,62,95,155,190,310,589,1178,2945,5890

Greatest Common Factor

We found the factors 1582,5890 . The biggest common factor number is the GCF number.
So the greatest common factor 1582,5890 is 2.

Lets's calculate LCM of 254,7601

Lowest Common Multiple of 254,7601 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1930654

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1930654

Therefore, the GCF of Fractions 1582/254,5890/7601 is 2/1930654

Least Common Multiple of 254,7601 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 254,7601 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(254,7601) = 1

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

GCF(254,7601) x common factors =1 x 1 = 1

LCM(254,7601) = ( 254 × 7601 ) / 1

LCM(254,7601) = 1930654 / 1

LCM(254,7601) = 1930654

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FAQs on GCF of Fractions of 1582/254, 5890/7601

1. What is the HCF of 1582,5890?

The HCF of 1582,5890 is 2

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 1582/254, 5890/7601?

Answer: GCF of Numerators as per given numbers 1582/254, 5890/7601 is

GCF of Numerators i.e. for 1582,5890 is 2

LCM of denominators i.e. for 254,7601 is 1930654.

Thus, GCF of Fractions is 2/1930654.Finally, GCF of Fractions for 1582/254, 5890/7601 is 2/1930654.