GCF of 683/400, 7738/100
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 683/400, 7738/100 i.e 1/400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 683/400, 7738/100.
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 683/400,7738/100?
Given fractions are 683/400,7738/100
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 683/400,7738/100, numerators are 683,7738
Denominators are 400,100
The GCF of 683,7738 is 1 .
LCM of 400,100 is 400.
The greatest common factor of 683/400,7738/100 = [GCF of 683,7738]/[LCM of 400,100]= 1/400
Therefore, the GCF of 683/400,7738/100 is 1/400.
To find the highest common factor of 683,7738, we have to find the factors of both numbers and list the highest common factor.
The factors of 683 are 1, 683
The factors of 7738 are 1, 2, 53, 73, 106, 146, 3869, 7738
The HCF of 683,7738 is 1.
Lets's calculate GCF of 683,7738
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 683,7738 By Matching Biggest Common Factor Method
Now, list down the factors of 683
:1,683
Now, list down the factors of 7738
:1,2,53,73,106,146,3869,7738
Greatest Common Factor
We found the factors 683,7738 . The biggest common factor number is the GCF number.
So the greatest common factor 683,7738 is 1.
Lets's calculate LCM of 400,100
| 2 | 400, 100 |
| 2 | 200, 50 |
| 5 | 100, 25 |
| 5 | 20, 5 |
| 4, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 5 x 4 x 1 = 400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/400
Therefore, the GCF of Fractions 683/400,7738/100 is 1/400
Least Common Multiple of 400,100 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 400,100 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(400,100) = 100
common factors(in case of two or more numbers have common factors) = 1
GCF(400,100) x common factors =100 x 1 = 100
LCM(400,100) = ( 400 × 100 ) / 100
LCM(400,100) = 40000 / 100
LCM(400,100) = 400
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FAQs on GCF of Fractions of 683/400, 7738/100
1. What is the HCF of 683,7738?
The HCF of 683,7738 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 683/400, 7738/100?
Answer: GCF of Numerators as per given numbers 683/400, 7738/100 is
GCF of Numerators i.e. for 683,7738 is 1
LCM of denominators i.e. for 400,100 is 400.
Thus, GCF of Fractions is 1/400.Finally, GCF of Fractions for 683/400, 7738/100 is 1/400.