GCF of 51/40, 74/88, 75/120
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 51/40, 74/88, 75/120 i.e 1/1320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/40, 74/88, 75/120.
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 51/40,74/88,75/120?
Given fractions are 51/40,74/88,75/120
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 51/40,74/88,75/120, numerators are 51,74,75
Denominators are 40,88,120
The GCF of 51,74,75 is 1 .
LCM of 40,88,120 is 1320.
The greatest common factor of 51/40,74/88,75/120 = [GCF of 51,74,75]/[LCM of 40,88,120]= 1/1320
Therefore, the GCF of 51/40,74/88,75/120 is 1/1320.
To find the highest common factor of 51,74,75, we have to find the factors of both numbers and list the highest common factor.
The factors of 51 are 1, 3, 17, 51
The factors of 74 are 1, 2, 37, 74
The factors of 75 are 1, 3, 5, 15, 25, 75
The HCF of 51,74,75 is 1.
Lets's calculate GCF of 51,74,75
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 51,74,75 By Matching Biggest Common Factor Method
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 75
:1,3,5,15,25,75
Greatest Common Factor
We found the factors 51,74,75 . The biggest common factor number is the GCF number.
So the greatest common factor 51,74,75 is 1.
Lets's calculate LCM of 40,88,120
| 2 | 40, 88, 120 |
| 2 | 20, 44, 60 |
| 2 | 10, 22, 30 |
| 5 | 5, 11, 15 |
| 1, 11, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 1 x 11 x 3 = 1320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1320
Therefore, the GCF of Fractions 51/40,74/88,75/120 is 1/1320
Least Common Multiple of 40,88,120 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 40,88,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,88,120) = 8
common factors(in case of two or more numbers have common factors) = 40
GCF(40,88,120) x common factors =8 x 40 = 320
LCM(40,88,120) = ( 40 × 88 × 120 ) / 320
LCM(40,88,120) = 422400 / 320
LCM(40,88,120) = 1320
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 51/40, 74/88, 75/120
1. What is the HCF of 51,74,75?
The HCF of 51,74,75 is 1
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 51/40, 74/88, 75/120?
Answer: GCF of Numerators as per given numbers 51/40, 74/88, 75/120 is
GCF of Numerators i.e. for 51,74,75 is 1
LCM of denominators i.e. for 40,88,120 is 1320.
Thus, GCF of Fractions is 1/1320.Finally, GCF of Fractions for 51/40, 74/88, 75/120 is 1/1320.