GCF of 262/414, 2272/125
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 262/414, 2272/125 i.e 2/51750 easily. The following is the detailed procedure to determine the greatest common factor of fractions 262/414, 2272/125.
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 262/414,2272/125?
Given fractions are 262/414,2272/125
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 262/414,2272/125, numerators are 262,2272
Denominators are 414,125
The GCF of 262,2272 is 2 .
LCM of 414,125 is 51750.
The greatest common factor of 262/414,2272/125 = [GCF of 262,2272]/[LCM of 414,125]= 2/51750
Therefore, the GCF of 262/414,2272/125 is 2/51750.
To find the highest common factor of 262,2272, we have to find the factors of both numbers and list the highest common factor.
The factors of 262 are 1, 2, 131, 262
The factors of 2272 are 1, 2, 4, 8, 16, 32, 71, 142, 284, 568, 1136, 2272
The HCF of 262,2272 is 2.
Lets's calculate GCF of 262,2272
| 2 | 262, 2272 |
| 131, 1136 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 262,2272 By Matching Biggest Common Factor Method
Now, list down the factors of 262
:1,2,131,262
Now, list down the factors of 2272
:1,2,4,8,16,32,71,142,284,568,1136,2272
Greatest Common Factor
We found the factors 262,2272 . The biggest common factor number is the GCF number.
So the greatest common factor 262,2272 is 2.
Lets's calculate LCM of 414,125
Given numbers has no common factors except 1. So, there LCM is their product i.e 51750
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/51750
Therefore, the GCF of Fractions 262/414,2272/125 is 2/51750
Least Common Multiple of 414,125 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 414,125 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,125) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(414,125) x common factors =1 x 1 = 1
LCM(414,125) = ( 414 × 125 ) / 1
LCM(414,125) = 51750 / 1
LCM(414,125) = 51750
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FAQs on GCF of Fractions of 262/414, 2272/125
1. What is the HCF of 262,2272?
The HCF of 262,2272 is 2
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 262/414, 2272/125?
Answer: GCF of Numerators as per given numbers 262/414, 2272/125 is
GCF of Numerators i.e. for 262,2272 is 2
LCM of denominators i.e. for 414,125 is 51750.
Thus, GCF of Fractions is 2/51750.Finally, GCF of Fractions for 262/414, 2272/125 is 2/51750.