How to Find GCF of 400/70, 448/765?

GCF of 400/70, 448/765

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 400/70, 448/765 i.e 16/10710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 400/70, 448/765.

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 400/70,448/765?

Given fractions are 400/70,448/765

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 400/70,448/765, numerators are 400,448

Denominators are 70,765

The GCF of 400,448 is 16 .

LCM of 70,765 is 10710.

The greatest common factor of 400/70,448/765 = [GCF of 400,448]/[LCM of 70,765]= 16/10710

Therefore, the GCF of 400/70,448/765 is 16/10710.

Greatest Common Factor of 400,448

To find the highest common factor of 400,448, we have to find the factors of both numbers and list the highest common factor.

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448

The HCF of 400,448 is 16.

Lets's calculate GCF of 400,448

Greatest Common Factor (GCF) of 400,448 By Common Division

2	400, 448
2	200, 224
2	100, 112
2	50, 56
	25, 28

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 400,448 By Matching Biggest Common Factor Method

Now, list down the factors of 400

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Now, list down the factors of 448

1,2,4,7,8,14,16,28,32,56,64,112,224,448

Greatest Common Factor

We found the factors 400,448 . The biggest common factor number is the GCF number.
So the greatest common factor 400,448 is 16.

Lets's calculate LCM of 70,765

Lowest Common Multiple of 70,765 using Common Division

5	70, 765
	14, 153

∴ So the LCM of the given numbers is 5 x 14 x 153 = 10710

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/10710

Therefore, the GCF of Fractions 400/70,448/765 is 16/10710

Least Common Multiple of 70,765 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 70,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,765) = 5

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

GCF(70,765) x common factors =5 x 1 = 5

LCM(70,765) = ( 70 × 765 ) / 5

LCM(70,765) = 53550 / 5

LCM(70,765) = 10710

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FAQs on GCF of Fractions of 400/70, 448/765

1. What is the HCF of 400,448?

The HCF of 400,448 is 16

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 400/70, 448/765?

Answer: GCF of Numerators as per given numbers 400/70, 448/765 is

GCF of Numerators i.e. for 400,448 is 16

LCM of denominators i.e. for 70,765 is 10710.

Thus, GCF of Fractions is 16/10710.Finally, GCF of Fractions for 400/70, 448/765 is 16/10710.