GCF of 738/144, 416/800
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 738/144, 416/800 i.e 2/7200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 738/144, 416/800.
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 738/144,416/800?
Given fractions are 738/144,416/800
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 738/144,416/800, numerators are 738,416
Denominators are 144,800
The GCF of 738,416 is 2 .
LCM of 144,800 is 7200.
The greatest common factor of 738/144,416/800 = [GCF of 738,416]/[LCM of 144,800]= 2/7200
Therefore, the GCF of 738/144,416/800 is 2/7200.
To find the highest common factor of 738,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 738,416 is 2.
Lets's calculate GCF of 738,416
| 2 | 738, 416 |
| 369, 208 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 738,416 By Matching Biggest Common Factor Method
Now, list down the factors of 738
:1,2,3,6,9,18,41,82,123,246,369,738
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 738,416 . The biggest common factor number is the GCF number.
So the greatest common factor 738,416 is 2.
Lets's calculate LCM of 144,800
| 2 | 144, 800 |
| 2 | 72, 400 |
| 2 | 36, 200 |
| 2 | 18, 100 |
| 9, 50 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 9 x 50 = 7200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7200
Therefore, the GCF of Fractions 738/144,416/800 is 2/7200
Least Common Multiple of 144,800 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 144,800 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(144,800) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(144,800) x common factors =16 x 1 = 16
LCM(144,800) = ( 144 × 800 ) / 16
LCM(144,800) = 115200 / 16
LCM(144,800) = 7200
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FAQs on GCF of Fractions of 738/144, 416/800
1. What is the HCF of 738,416?
The HCF of 738,416 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 738/144, 416/800?
Answer: GCF of Numerators as per given numbers 738/144, 416/800 is
GCF of Numerators i.e. for 738,416 is 2
LCM of denominators i.e. for 144,800 is 7200.
Thus, GCF of Fractions is 2/7200.Finally, GCF of Fractions for 738/144, 416/800 is 2/7200.