GCF of 722/69, 456/3413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 722/69, 456/3413 i.e 38/235497 easily. The following is the detailed procedure to determine the greatest common factor of fractions 722/69, 456/3413.
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 722/69,456/3413?
Given fractions are 722/69,456/3413
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 722/69,456/3413, numerators are 722,456
Denominators are 69,3413
The GCF of 722,456 is 38 .
LCM of 69,3413 is 235497.
The greatest common factor of 722/69,456/3413 = [GCF of 722,456]/[LCM of 69,3413]= 38/235497
Therefore, the GCF of 722/69,456/3413 is 38/235497.
To find the highest common factor of 722,456, 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 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 722,456 is 38.
Lets's calculate GCF of 722,456
| 2 | 722, 456 |
| 19 | 361, 228 |
| 19, 12 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 722,456 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 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 722,456 . The biggest common factor number is the GCF number.
So the greatest common factor 722,456 is 38.
Lets's calculate LCM of 69,3413
Given numbers has no common factors except 1. So, there LCM is their product i.e 235497
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/235497
Therefore, the GCF of Fractions 722/69,456/3413 is 38/235497
Least Common Multiple of 69,3413 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 69,3413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,3413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(69,3413) x common factors =1 x 1 = 1
LCM(69,3413) = ( 69 × 3413 ) / 1
LCM(69,3413) = 235497 / 1
LCM(69,3413) = 235497
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FAQs on GCF of Fractions of 722/69, 456/3413
1. What is the HCF of 722,456?
The HCF of 722,456 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 722/69, 456/3413?
Answer: GCF of Numerators as per given numbers 722/69, 456/3413 is
GCF of Numerators i.e. for 722,456 is 38
LCM of denominators i.e. for 69,3413 is 235497.
Thus, GCF of Fractions is 38/235497.Finally, GCF of Fractions for 722/69, 456/3413 is 38/235497.