Highest Common Factor of 2109, 318 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, 318 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2109, 318 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, 318 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, 318 is 3.
HCF(2109, 318) = 3
HCF of 2109, 318 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, 318 is 3.
Highest Common Factor of 2109,318 is 3
Step 1: Since 2109 > 318, we apply the division lemma to 2109 and 318, to get
2109 = 318 x 6 + 201
Step 2: Since the reminder 318 ≠ 0, we apply division lemma to 201 and 318, to get
318 = 201 x 1 + 117
Step 3: We consider the new divisor 201 and the new remainder 117, and apply the division lemma to get
201 = 117 x 1 + 84
We consider the new divisor 117 and the new remainder 84,and apply the division lemma to get
117 = 84 x 1 + 33
We consider the new divisor 84 and the new remainder 33,and apply the division lemma to get
84 = 33 x 2 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2109 and 318 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(84,33) = HCF(117,84) = HCF(201,117) = HCF(318,201) = HCF(2109,318) .
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Frequently Asked Questions on HCF of 2109, 318 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, 318?
Answer: HCF of 2109, 318 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2109, 318 using Euclid's Algorithm?
Answer: For arbitrary numbers 2109, 318 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.