GCF of 228/32, 278/750
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 228/32, 278/750 i.e 2/12000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 228/32, 278/750.
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 228/32,278/750?
Given fractions are 228/32,278/750
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 228/32,278/750, numerators are 228,278
Denominators are 32,750
The GCF of 228,278 is 2 .
LCM of 32,750 is 12000.
The greatest common factor of 228/32,278/750 = [GCF of 228,278]/[LCM of 32,750]= 2/12000
Therefore, the GCF of 228/32,278/750 is 2/12000.
To find the highest common factor of 228,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The factors of 278 are 1, 2, 139, 278
The HCF of 228,278 is 2.
Lets's calculate GCF of 228,278
| 2 | 228, 278 |
| 114, 139 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 228,278 By Matching Biggest Common Factor Method
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 228,278 . The biggest common factor number is the GCF number.
So the greatest common factor 228,278 is 2.
Lets's calculate LCM of 32,750
| 2 | 32, 750 |
| 16, 375 |
∴ So the LCM of the given numbers is 2 x 16 x 375 = 12000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12000
Therefore, the GCF of Fractions 228/32,278/750 is 2/12000
Least Common Multiple of 32,750 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 32,750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,750) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,750) x common factors =2 x 1 = 2
LCM(32,750) = ( 32 × 750 ) / 2
LCM(32,750) = 24000 / 2
LCM(32,750) = 12000
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FAQs on GCF of Fractions of 228/32, 278/750
1. What is the HCF of 228,278?
The HCF of 228,278 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 228/32, 278/750?
Answer: GCF of Numerators as per given numbers 228/32, 278/750 is
GCF of Numerators i.e. for 228,278 is 2
LCM of denominators i.e. for 32,750 is 12000.
Thus, GCF of Fractions is 2/12000.Finally, GCF of Fractions for 228/32, 278/750 is 2/12000.