How to Find GCF of 416/469, 7170/661?

GCF of 416/469, 7170/661

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 416/469, 7170/661 i.e 2/310009 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/469, 7170/661.

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 416/469,7170/661?

Given fractions are 416/469,7170/661

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 416/469,7170/661, numerators are 416,7170

Denominators are 469,661

The GCF of 416,7170 is 2 .

LCM of 469,661 is 310009.

The greatest common factor of 416/469,7170/661 = [GCF of 416,7170]/[LCM of 469,661]= 2/310009

Therefore, the GCF of 416/469,7170/661 is 2/310009.

Greatest Common Factor of 416,7170

To find the highest common factor of 416,7170, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 7170 are 1, 2, 3, 5, 6, 10, 15, 30, 239, 478, 717, 1195, 1434, 2390, 3585, 7170

The HCF of 416,7170 is 2.

Lets's calculate GCF of 416,7170

Greatest Common Factor (GCF) of 416,7170 By Common Division

2	416, 7170
	208, 3585

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

Greatest Common Factor of 416,7170 By Matching Biggest Common Factor Method

Now, list down the factors of 416

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

Now, list down the factors of 7170

1,2,3,5,6,10,15,30,239,478,717,1195,1434,2390,3585,7170

Greatest Common Factor

We found the factors 416,7170 . The biggest common factor number is the GCF number.
So the greatest common factor 416,7170 is 2.

Lets's calculate LCM of 469,661

Lowest Common Multiple of 469,661 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 310009

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/310009

Therefore, the GCF of Fractions 416/469,7170/661 is 2/310009

Least Common Multiple of 469,661 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 469,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(469,661) = 1

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

GCF(469,661) x common factors =1 x 1 = 1

LCM(469,661) = ( 469 × 661 ) / 1

LCM(469,661) = 310009 / 1

LCM(469,661) = 310009

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FAQs on GCF of Fractions of 416/469, 7170/661

1. What is the HCF of 416,7170?

The HCF of 416,7170 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 416/469, 7170/661?

Answer: GCF of Numerators as per given numbers 416/469, 7170/661 is

GCF of Numerators i.e. for 416,7170 is 2

LCM of denominators i.e. for 469,661 is 310009.

Thus, GCF of Fractions is 2/310009.Finally, GCF of Fractions for 416/469, 7170/661 is 2/310009.