Highest Common Factor of 694, 406 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 694, 406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 694, 406 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 694, 406 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 694, 406 is 2.
HCF(694, 406) = 2
HCF of 694, 406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 694, 406 is 2.
Highest Common Factor of 694,406 is 2
Step 1: Since 694 > 406, we apply the division lemma to 694 and 406, to get
694 = 406 x 1 + 288
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 288 and 406, to get
406 = 288 x 1 + 118
Step 3: We consider the new divisor 288 and the new remainder 118, and apply the division lemma to get
288 = 118 x 2 + 52
We consider the new divisor 118 and the new remainder 52,and apply the division lemma to get
118 = 52 x 2 + 14
We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get
52 = 14 x 3 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 694 and 406 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(118,52) = HCF(288,118) = HCF(406,288) = HCF(694,406) .
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Frequently Asked Questions on HCF of 694, 406 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 694, 406?
Answer: HCF of 694, 406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 694, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 694, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.