GCF of 722/85, 760/914
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 722/85, 760/914 i.e 38/77690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 722/85, 760/914.
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 722/85,760/914?
Given fractions are 722/85,760/914
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 722/85,760/914, numerators are 722,760
Denominators are 85,914
The GCF of 722,760 is 38 .
LCM of 85,914 is 77690.
The greatest common factor of 722/85,760/914 = [GCF of 722,760]/[LCM of 85,914]= 38/77690
Therefore, the GCF of 722/85,760/914 is 38/77690.
To find the highest common factor of 722,760, we have to find the factors of both numbers and list the highest common factor.
The factors of 722 are 1, 2, 19, 38, 361, 722
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The HCF of 722,760 is 38.
Lets's calculate GCF of 722,760
| 2 | 722, 760 |
| 19 | 361, 380 |
| 19, 20 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 722,760 By Matching Biggest Common Factor Method
Now, list down the factors of 722
:1,2,19,38,361,722
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Greatest Common Factor
We found the factors 722,760 . The biggest common factor number is the GCF number.
So the greatest common factor 722,760 is 38.
Lets's calculate LCM of 85,914
Given numbers has no common factors except 1. So, there LCM is their product i.e 77690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/77690
Therefore, the GCF of Fractions 722/85,760/914 is 38/77690
Least Common Multiple of 85,914 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 85,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,914) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(85,914) x common factors =1 x 1 = 1
LCM(85,914) = ( 85 × 914 ) / 1
LCM(85,914) = 77690 / 1
LCM(85,914) = 77690
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FAQs on GCF of Fractions of 722/85, 760/914
1. What is the HCF of 722,760?
The HCF of 722,760 is 38
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 722/85, 760/914?
Answer: GCF of Numerators as per given numbers 722/85, 760/914 is
GCF of Numerators i.e. for 722,760 is 38
LCM of denominators i.e. for 85,914 is 77690.
Thus, GCF of Fractions is 38/77690.Finally, GCF of Fractions for 722/85, 760/914 is 38/77690.