GCF of 1406/708, 1754/9702
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1406/708, 1754/9702 i.e 2/1144836 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1406/708, 1754/9702.
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 1406/708,1754/9702?
Given fractions are 1406/708,1754/9702
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 1406/708,1754/9702, numerators are 1406,1754
Denominators are 708,9702
The GCF of 1406,1754 is 2 .
LCM of 708,9702 is 1144836.
The greatest common factor of 1406/708,1754/9702 = [GCF of 1406,1754]/[LCM of 708,9702]= 2/1144836
Therefore, the GCF of 1406/708,1754/9702 is 2/1144836.
To find the highest common factor of 1406,1754, we have to find the factors of both numbers and list the highest common factor.
The factors of 1406 are 1, 2, 19, 37, 38, 74, 703, 1406
The factors of 1754 are 1, 2, 877, 1754
The HCF of 1406,1754 is 2.
Lets's calculate GCF of 1406,1754
| 2 | 1406, 1754 |
| 703, 877 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1406,1754 By Matching Biggest Common Factor Method
Now, list down the factors of 1406
:1,2,19,37,38,74,703,1406
Now, list down the factors of 1754
:1,2,877,1754
Greatest Common Factor
We found the factors 1406,1754 . The biggest common factor number is the GCF number.
So the greatest common factor 1406,1754 is 2.
Lets's calculate LCM of 708,9702
| 2 | 708, 9702 |
| 3 | 354, 4851 |
| 118, 1617 |
∴ So the LCM of the given numbers is 2 x 3 x 118 x 1617 = 1144836
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1144836
Therefore, the GCF of Fractions 1406/708,1754/9702 is 2/1144836
Least Common Multiple of 708,9702 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 708,9702 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(708,9702) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(708,9702) x common factors =6 x 1 = 6
LCM(708,9702) = ( 708 × 9702 ) / 6
LCM(708,9702) = 6869016 / 6
LCM(708,9702) = 1144836
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FAQs on GCF of Fractions of 1406/708, 1754/9702
1. What is the HCF of 1406,1754?
The HCF of 1406,1754 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 1406/708, 1754/9702?
Answer: GCF of Numerators as per given numbers 1406/708, 1754/9702 is
GCF of Numerators i.e. for 1406,1754 is 2
LCM of denominators i.e. for 708,9702 is 1144836.
Thus, GCF of Fractions is 2/1144836.Finally, GCF of Fractions for 1406/708, 1754/9702 is 2/1144836.