GCF of 722/85, 304/204
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, 304/204 i.e 38/1020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 722/85, 304/204.
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 722/85,304/204?
Given fractions are 722/85,304/204
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 722/85,304/204, numerators are 722,304
Denominators are 85,204
The GCF of 722,304 is 38 .
LCM of 85,204 is 1020.
The greatest common factor of 722/85,304/204 = [GCF of 722,304]/[LCM of 85,204]= 38/1020
Therefore, the GCF of 722/85,304/204 is 38/1020.
To find the highest common factor of 722,304, 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 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
The HCF of 722,304 is 38.
Lets's calculate GCF of 722,304
| 2 | 722, 304 |
| 19 | 361, 152 |
| 19, 8 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 722,304 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 304
:1,2,4,8,16,19,38,76,152,304
Greatest Common Factor
We found the factors 722,304 . The biggest common factor number is the GCF number.
So the greatest common factor 722,304 is 38.
Lets's calculate LCM of 85,204
| 17 | 85, 204 |
| 5, 12 |
∴ So the LCM of the given numbers is 17 x 5 x 12 = 1020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/1020
Therefore, the GCF of Fractions 722/85,304/204 is 38/1020
Least Common Multiple of 85,204 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 85,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,204) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(85,204) x common factors =17 x 1 = 17
LCM(85,204) = ( 85 × 204 ) / 17
LCM(85,204) = 17340 / 17
LCM(85,204) = 1020
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FAQs on GCF of Fractions of 722/85, 304/204
1. What is the HCF of 722,304?
The HCF of 722,304 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, 304/204?
Answer: GCF of Numerators as per given numbers 722/85, 304/204 is
GCF of Numerators i.e. for 722,304 is 38
LCM of denominators i.e. for 85,204 is 1020.
Thus, GCF of Fractions is 38/1020.Finally, GCF of Fractions for 722/85, 304/204 is 38/1020.