GCF of 705/76, 775/19, 784/84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 705/76, 775/19, 784/84 i.e 1/1596 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/76, 775/19, 784/84.
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 705/76,775/19,784/84?
Given fractions are 705/76,775/19,784/84
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 705/76,775/19,784/84, numerators are 705,775,784
Denominators are 76,19,84
The GCF of 705,775,784 is 1 .
LCM of 76,19,84 is 1596.
The greatest common factor of 705/76,775/19,784/84 = [GCF of 705,775,784]/[LCM of 76,19,84]= 1/1596
Therefore, the GCF of 705/76,775/19,784/84 is 1/1596.
To find the highest common factor of 705,775,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 775 are 1, 5, 25, 31, 155, 775
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 705,775,784 is 1.
Lets's calculate GCF of 705,775,784
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 705,775,784 By Matching Biggest Common Factor Method
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 775
:1,5,25,31,155,775
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 705,775,784 . The biggest common factor number is the GCF number.
So the greatest common factor 705,775,784 is 1.
Lets's calculate LCM of 76,19,84
| 2 | 76, 19, 84 |
| 2 | 38, 19, 42 |
| 19 | 19, 19, 21 |
| 1, 1, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 19 x 1 x 1 x 21 = 1596
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1596
Therefore, the GCF of Fractions 705/76,775/19,784/84 is 1/1596
Least Common Multiple of 76,19,84 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 76,19,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,19,84) = 1
common factors(in case of two or more numbers have common factors) = 76
GCF(76,19,84) x common factors =1 x 76 = 76
LCM(76,19,84) = ( 76 × 19 × 84 ) / 76
LCM(76,19,84) = 121296 / 76
LCM(76,19,84) = 1596
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FAQs on GCF of Fractions of 705/76, 775/19, 784/84
1. What is the HCF of 705,775,784?
The HCF of 705,775,784 is 1
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 705/76, 775/19, 784/84?
Answer: GCF of Numerators as per given numbers 705/76, 775/19, 784/84 is
GCF of Numerators i.e. for 705,775,784 is 1
LCM of denominators i.e. for 76,19,84 is 1596.
Thus, GCF of Fractions is 1/1596.Finally, GCF of Fractions for 705/76, 775/19, 784/84 is 1/1596.