GCF of 722/720, 345/306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 722/720, 345/306 i.e 1/12240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 722/720, 345/306.
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 722/720,345/306?
Given fractions are 722/720,345/306
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 722/720,345/306, numerators are 722,345
Denominators are 720,306
The GCF of 722,345 is 1 .
LCM of 720,306 is 12240.
The greatest common factor of 722/720,345/306 = [GCF of 722,345]/[LCM of 720,306]= 1/12240
Therefore, the GCF of 722/720,345/306 is 1/12240.
To find the highest common factor of 722,345, 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 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 722,345 is 1.
Lets's calculate GCF of 722,345
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 722,345 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 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 722,345 . The biggest common factor number is the GCF number.
So the greatest common factor 722,345 is 1.
Lets's calculate LCM of 720,306
| 2 | 720, 306 |
| 3 | 360, 153 |
| 3 | 120, 51 |
| 40, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 40 x 17 = 12240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12240
Therefore, the GCF of Fractions 722/720,345/306 is 1/12240
Least Common Multiple of 720,306 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 720,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(720,306) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(720,306) x common factors =18 x 1 = 18
LCM(720,306) = ( 720 × 306 ) / 18
LCM(720,306) = 220320 / 18
LCM(720,306) = 12240
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FAQs on GCF of Fractions of 722/720, 345/306
1. What is the HCF of 722,345?
The HCF of 722,345 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 722/720, 345/306?
Answer: GCF of Numerators as per given numbers 722/720, 345/306 is
GCF of Numerators i.e. for 722,345 is 1
LCM of denominators i.e. for 720,306 is 12240.
Thus, GCF of Fractions is 1/12240.Finally, GCF of Fractions for 722/720, 345/306 is 1/12240.