GCF of 784/69, 456/9576
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/69, 456/9576 i.e 8/220248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/69, 456/9576.
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 784/69,456/9576?
Given fractions are 784/69,456/9576
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 784/69,456/9576, numerators are 784,456
Denominators are 69,9576
The GCF of 784,456 is 8 .
LCM of 69,9576 is 220248.
The greatest common factor of 784/69,456/9576 = [GCF of 784,456]/[LCM of 69,9576]= 8/220248
Therefore, the GCF of 784/69,456/9576 is 8/220248.
To find the highest common factor of 784,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 784,456 is 8.
Lets's calculate GCF of 784,456
| 2 | 784, 456 |
| 2 | 392, 228 |
| 2 | 196, 114 |
| 98, 57 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 784,456 By Matching Biggest Common Factor Method
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 784,456 . The biggest common factor number is the GCF number.
So the greatest common factor 784,456 is 8.
Lets's calculate LCM of 69,9576
| 3 | 69, 9576 |
| 23, 3192 |
∴ So the LCM of the given numbers is 3 x 23 x 3192 = 220248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/220248
Therefore, the GCF of Fractions 784/69,456/9576 is 8/220248
Least Common Multiple of 69,9576 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 69,9576 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,9576) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,9576) x common factors =3 x 1 = 3
LCM(69,9576) = ( 69 × 9576 ) / 3
LCM(69,9576) = 660744 / 3
LCM(69,9576) = 220248
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FAQs on GCF of Fractions of 784/69, 456/9576
1. What is the HCF of 784,456?
The HCF of 784,456 is 8
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 784/69, 456/9576?
Answer: GCF of Numerators as per given numbers 784/69, 456/9576 is
GCF of Numerators i.e. for 784,456 is 8
LCM of denominators i.e. for 69,9576 is 220248.
Thus, GCF of Fractions is 8/220248.Finally, GCF of Fractions for 784/69, 456/9576 is 8/220248.