GCF of 1748/784, 5730/1513
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1748/784, 5730/1513 i.e 2/1186192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1748/784, 5730/1513.
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 1748/784,5730/1513?
Given fractions are 1748/784,5730/1513
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 1748/784,5730/1513, numerators are 1748,5730
Denominators are 784,1513
The GCF of 1748,5730 is 2 .
LCM of 784,1513 is 1186192.
The greatest common factor of 1748/784,5730/1513 = [GCF of 1748,5730]/[LCM of 784,1513]= 2/1186192
Therefore, the GCF of 1748/784,5730/1513 is 2/1186192.
To find the highest common factor of 1748,5730, we have to find the factors of both numbers and list the highest common factor.
The factors of 1748 are 1, 2, 4, 19, 23, 38, 46, 76, 92, 437, 874, 1748
The factors of 5730 are 1, 2, 3, 5, 6, 10, 15, 30, 191, 382, 573, 955, 1146, 1910, 2865, 5730
The HCF of 1748,5730 is 2.
Lets's calculate GCF of 1748,5730
| 2 | 1748, 5730 |
| 874, 2865 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1748,5730 By Matching Biggest Common Factor Method
Now, list down the factors of 1748
:1,2,4,19,23,38,46,76,92,437,874,1748
Now, list down the factors of 5730
:1,2,3,5,6,10,15,30,191,382,573,955,1146,1910,2865,5730
Greatest Common Factor
We found the factors 1748,5730 . The biggest common factor number is the GCF number.
So the greatest common factor 1748,5730 is 2.
Lets's calculate LCM of 784,1513
Given numbers has no common factors except 1. So, there LCM is their product i.e 1186192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1186192
Therefore, the GCF of Fractions 1748/784,5730/1513 is 2/1186192
Least Common Multiple of 784,1513 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 784,1513 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(784,1513) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(784,1513) x common factors =1 x 1 = 1
LCM(784,1513) = ( 784 × 1513 ) / 1
LCM(784,1513) = 1186192 / 1
LCM(784,1513) = 1186192
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FAQs on GCF of Fractions of 1748/784, 5730/1513
1. What is the HCF of 1748,5730?
The HCF of 1748,5730 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 1748/784, 5730/1513?
Answer: GCF of Numerators as per given numbers 1748/784, 5730/1513 is
GCF of Numerators i.e. for 1748,5730 is 2
LCM of denominators i.e. for 784,1513 is 1186192.
Thus, GCF of Fractions is 2/1186192.Finally, GCF of Fractions for 1748/784, 5730/1513 is 2/1186192.