GCF of 768/58, 224/5266
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 768/58, 224/5266 i.e 32/152714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/58, 224/5266.
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 768/58,224/5266?
Given fractions are 768/58,224/5266
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 768/58,224/5266, numerators are 768,224
Denominators are 58,5266
The GCF of 768,224 is 32 .
LCM of 58,5266 is 152714.
The greatest common factor of 768/58,224/5266 = [GCF of 768,224]/[LCM of 58,5266]= 32/152714
Therefore, the GCF of 768/58,224/5266 is 32/152714.
To find the highest common factor of 768,224, we have to find the factors of both numbers and list the highest common factor.
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
The HCF of 768,224 is 32.
Lets's calculate GCF of 768,224
| 2 | 768, 224 |
| 2 | 384, 112 |
| 2 | 192, 56 |
| 2 | 96, 28 |
| 2 | 48, 14 |
| 24, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 768,224 By Matching Biggest Common Factor Method
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Now, list down the factors of 224
:1,2,4,7,8,14,16,28,32,56,112,224
Greatest Common Factor
We found the factors 768,224 . The biggest common factor number is the GCF number.
So the greatest common factor 768,224 is 32.
Lets's calculate LCM of 58,5266
| 2 | 58, 5266 |
| 29, 2633 |
∴ So the LCM of the given numbers is 2 x 29 x 2633 = 152714
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/152714
Therefore, the GCF of Fractions 768/58,224/5266 is 32/152714
Least Common Multiple of 58,5266 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 58,5266 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,5266) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(58,5266) x common factors =2 x 1 = 2
LCM(58,5266) = ( 58 × 5266 ) / 2
LCM(58,5266) = 305428 / 2
LCM(58,5266) = 152714
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FAQs on GCF of Fractions of 768/58, 224/5266
1. What is the HCF of 768,224?
The HCF of 768,224 is 32
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 768/58, 224/5266?
Answer: GCF of Numerators as per given numbers 768/58, 224/5266 is
GCF of Numerators i.e. for 768,224 is 32
LCM of denominators i.e. for 58,5266 is 152714.
Thus, GCF of Fractions is 32/152714.Finally, GCF of Fractions for 768/58, 224/5266 is 32/152714.