GCF of 1008/549, 2076/1412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1008/549, 2076/1412 i.e 12/775188 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1008/549, 2076/1412.
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 1008/549,2076/1412?
Given fractions are 1008/549,2076/1412
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 1008/549,2076/1412, numerators are 1008,2076
Denominators are 549,1412
The GCF of 1008,2076 is 12 .
LCM of 549,1412 is 775188.
The greatest common factor of 1008/549,2076/1412 = [GCF of 1008,2076]/[LCM of 549,1412]= 12/775188
Therefore, the GCF of 1008/549,2076/1412 is 12/775188.
To find the highest common factor of 1008,2076, we have to find the factors of both numbers and list the highest common factor.
The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008
The factors of 2076 are 1, 2, 3, 4, 6, 12, 173, 346, 519, 692, 1038, 2076
The HCF of 1008,2076 is 12.
Lets's calculate GCF of 1008,2076
| 2 | 1008, 2076 |
| 2 | 504, 1038 |
| 3 | 252, 519 |
| 84, 173 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 1008,2076 By Matching Biggest Common Factor Method
Now, list down the factors of 1008
:1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,36,42,48,56,63,72,84,112,126,144,168,252,336,504,1008
Now, list down the factors of 2076
:1,2,3,4,6,12,173,346,519,692,1038,2076
Greatest Common Factor
We found the factors 1008,2076 . The biggest common factor number is the GCF number.
So the greatest common factor 1008,2076 is 12.
Lets's calculate LCM of 549,1412
Given numbers has no common factors except 1. So, there LCM is their product i.e 775188
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/775188
Therefore, the GCF of Fractions 1008/549,2076/1412 is 12/775188
Least Common Multiple of 549,1412 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 549,1412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(549,1412) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(549,1412) x common factors =1 x 1 = 1
LCM(549,1412) = ( 549 × 1412 ) / 1
LCM(549,1412) = 775188 / 1
LCM(549,1412) = 775188
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FAQs on GCF of Fractions of 1008/549, 2076/1412
1. What is the HCF of 1008,2076?
The HCF of 1008,2076 is 12
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 1008/549, 2076/1412?
Answer: GCF of Numerators as per given numbers 1008/549, 2076/1412 is
GCF of Numerators i.e. for 1008,2076 is 12
LCM of denominators i.e. for 549,1412 is 775188.
Thus, GCF of Fractions is 12/775188.Finally, GCF of Fractions for 1008/549, 2076/1412 is 12/775188.