How to Find GCF of 684/72, 416/682?

GCF of 684/72, 416/682

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 684/72, 416/682 i.e 4/24552 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/72, 416/682.

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 684/72,416/682?

Given fractions are 684/72,416/682

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 684/72,416/682, numerators are 684,416

Denominators are 72,682

The GCF of 684,416 is 4 .

LCM of 72,682 is 24552.

The greatest common factor of 684/72,416/682 = [GCF of 684,416]/[LCM of 72,682]= 4/24552

Therefore, the GCF of 684/72,416/682 is 4/24552.

Greatest Common Factor of 684,416

To find the highest common factor of 684,416, we have to find the factors of both numbers and list the highest common factor.

The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

The HCF of 684,416 is 4.

Lets's calculate GCF of 684,416

Greatest Common Factor (GCF) of 684,416 By Common Division

2	684, 416
2	342, 208
	171, 104

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

Greatest Common Factor of 684,416 By Matching Biggest Common Factor Method

Now, list down the factors of 684

1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684

Now, list down the factors of 416

1,2,4,8,13,16,26,32,52,104,208,416

Greatest Common Factor

We found the factors 684,416 . The biggest common factor number is the GCF number.
So the greatest common factor 684,416 is 4.

Lets's calculate LCM of 72,682

Lowest Common Multiple of 72,682 using Common Division

2	72, 682
	36, 341

∴ So the LCM of the given numbers is 2 x 36 x 341 = 24552

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/24552

Therefore, the GCF of Fractions 684/72,416/682 is 4/24552

Least Common Multiple of 72,682 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 72,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,682) = 2

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

GCF(72,682) x common factors =2 x 1 = 2

LCM(72,682) = ( 72 × 682 ) / 2

LCM(72,682) = 49104 / 2

LCM(72,682) = 24552

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FAQs on GCF of Fractions of 684/72, 416/682

1. What is the HCF of 684,416?

The HCF of 684,416 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 684/72, 416/682?

Answer: GCF of Numerators as per given numbers 684/72, 416/682 is

GCF of Numerators i.e. for 684,416 is 4

LCM of denominators i.e. for 72,682 is 24552.

Thus, GCF of Fractions is 4/24552.Finally, GCF of Fractions for 684/72, 416/682 is 4/24552.