GCF of 220/51, 278/7269
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 220/51, 278/7269 i.e 2/123573 easily. The following is the detailed procedure to determine the greatest common factor of fractions 220/51, 278/7269.
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 220/51,278/7269?
Given fractions are 220/51,278/7269
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 220/51,278/7269, numerators are 220,278
Denominators are 51,7269
The GCF of 220,278 is 2 .
LCM of 51,7269 is 123573.
The greatest common factor of 220/51,278/7269 = [GCF of 220,278]/[LCM of 51,7269]= 2/123573
Therefore, the GCF of 220/51,278/7269 is 2/123573.
To find the highest common factor of 220,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
The factors of 278 are 1, 2, 139, 278
The HCF of 220,278 is 2.
Lets's calculate GCF of 220,278
| 2 | 220, 278 |
| 110, 139 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 220,278 By Matching Biggest Common Factor Method
Now, list down the factors of 220
:1,2,4,5,10,11,20,22,44,55,110,220
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 220,278 . The biggest common factor number is the GCF number.
So the greatest common factor 220,278 is 2.
Lets's calculate LCM of 51,7269
| 3 | 51, 7269 |
| 17, 2423 |
∴ So the LCM of the given numbers is 3 x 17 x 2423 = 123573
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/123573
Therefore, the GCF of Fractions 220/51,278/7269 is 2/123573
Least Common Multiple of 51,7269 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 51,7269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,7269) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,7269) x common factors =3 x 1 = 3
LCM(51,7269) = ( 51 × 7269 ) / 3
LCM(51,7269) = 370719 / 3
LCM(51,7269) = 123573
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FAQs on GCF of Fractions of 220/51, 278/7269
1. What is the HCF of 220,278?
The HCF of 220,278 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 220/51, 278/7269?
Answer: GCF of Numerators as per given numbers 220/51, 278/7269 is
GCF of Numerators i.e. for 220,278 is 2
LCM of denominators i.e. for 51,7269 is 123573.
Thus, GCF of Fractions is 2/123573.Finally, GCF of Fractions for 220/51, 278/7269 is 2/123573.