Highest Common Factor of 2109, 3279 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 2109, 3279 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2109, 3279 is 3 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 2109, 3279 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 2109, 3279 is 3.
HCF(2109, 3279) = 3
HCF of 2109, 3279 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2109, 3279 is 3.
Highest Common Factor of 2109,3279 is 3
Step 1: Since 3279 > 2109, we apply the division lemma to 3279 and 2109, to get
3279 = 2109 x 1 + 1170
Step 2: Since the reminder 2109 ≠ 0, we apply division lemma to 1170 and 2109, to get
2109 = 1170 x 1 + 939
Step 3: We consider the new divisor 1170 and the new remainder 939, and apply the division lemma to get
1170 = 939 x 1 + 231
We consider the new divisor 939 and the new remainder 231,and apply the division lemma to get
939 = 231 x 4 + 15
We consider the new divisor 231 and the new remainder 15,and apply the division lemma to get
231 = 15 x 15 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2109 and 3279 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(231,15) = HCF(939,231) = HCF(1170,939) = HCF(2109,1170) = HCF(3279,2109) .
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Frequently Asked Questions on HCF of 2109, 3279 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 2109, 3279?
Answer: HCF of 2109, 3279 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2109, 3279 using Euclid's Algorithm?
Answer: For arbitrary numbers 2109, 3279 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.