Highest Common Factor of 406, 2694 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 406, 2694 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 406, 2694 is 2 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 406, 2694 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 406, 2694 is 2.
HCF(406, 2694) = 2
HCF of 406, 2694 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 406, 2694 is 2.
Highest Common Factor of 406,2694 is 2
Step 1: Since 2694 > 406, we apply the division lemma to 2694 and 406, to get
2694 = 406 x 6 + 258
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 258 and 406, to get
406 = 258 x 1 + 148
Step 3: We consider the new divisor 258 and the new remainder 148, and apply the division lemma to get
258 = 148 x 1 + 110
We consider the new divisor 148 and the new remainder 110,and apply the division lemma to get
148 = 110 x 1 + 38
We consider the new divisor 110 and the new remainder 38,and apply the division lemma to get
110 = 38 x 2 + 34
We consider the new divisor 38 and the new remainder 34,and apply the division lemma to get
38 = 34 x 1 + 4
We consider the new divisor 34 and the new remainder 4,and apply the division lemma to get
34 = 4 x 8 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 406 and 2694 is 2
Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(38,34) = HCF(110,38) = HCF(148,110) = HCF(258,148) = HCF(406,258) = HCF(2694,406) .
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Frequently Asked Questions on HCF of 406, 2694 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 406, 2694?
Answer: HCF of 406, 2694 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 406, 2694 using Euclid's Algorithm?
Answer: For arbitrary numbers 406, 2694 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
