How to Find GCF of 420/304, 7688/465?

GCF of 420/304, 7688/465

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 420/304, 7688/465 i.e 4/141360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/304, 7688/465.

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 420/304,7688/465?

Given fractions are 420/304,7688/465

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 420/304,7688/465, numerators are 420,7688

Denominators are 304,465

The GCF of 420,7688 is 4 .

LCM of 304,465 is 141360.

The greatest common factor of 420/304,7688/465 = [GCF of 420,7688]/[LCM of 304,465]= 4/141360

Therefore, the GCF of 420/304,7688/465 is 4/141360.

Greatest Common Factor of 420,7688

To find the highest common factor of 420,7688, we have to find the factors of both numbers and list the highest common factor.

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The factors of 7688 are 1, 2, 4, 8, 31, 62, 124, 248, 961, 1922, 3844, 7688

The HCF of 420,7688 is 4.

Lets's calculate GCF of 420,7688

Greatest Common Factor (GCF) of 420,7688 By Common Division

2	420, 7688
2	210, 3844
	105, 1922

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 420,7688 By Matching Biggest Common Factor Method

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Now, list down the factors of 7688

1,2,4,8,31,62,124,248,961,1922,3844,7688

Greatest Common Factor

We found the factors 420,7688 . The biggest common factor number is the GCF number.
So the greatest common factor 420,7688 is 4.

Lets's calculate LCM of 304,465

Lowest Common Multiple of 304,465 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 141360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/141360

Therefore, the GCF of Fractions 420/304,7688/465 is 4/141360

Least Common Multiple of 304,465 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 304,465 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(304,465) = 1

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

GCF(304,465) x common factors =1 x 1 = 1

LCM(304,465) = ( 304 × 465 ) / 1

LCM(304,465) = 141360 / 1

LCM(304,465) = 141360

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FAQs on GCF of Fractions of 420/304, 7688/465

1. What is the HCF of 420,7688?

The HCF of 420,7688 is 4

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 420/304, 7688/465?

Answer: GCF of Numerators as per given numbers 420/304, 7688/465 is

GCF of Numerators i.e. for 420,7688 is 4

LCM of denominators i.e. for 304,465 is 141360.

Thus, GCF of Fractions is 4/141360.Finally, GCF of Fractions for 420/304, 7688/465 is 4/141360.