Highest Common Factor of 689, 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 689, 406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 406 is 1 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 689, 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 689, 406 is 1.
HCF(689, 406) = 1
HCF of 689, 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 689, 406 is 1.
Highest Common Factor of 689,406 is 1
Step 1: Since 689 > 406, we apply the division lemma to 689 and 406, to get
689 = 406 x 1 + 283
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 283 and 406, to get
406 = 283 x 1 + 123
Step 3: We consider the new divisor 283 and the new remainder 123, and apply the division lemma to get
283 = 123 x 2 + 37
We consider the new divisor 123 and the new remainder 37,and apply the division lemma to get
123 = 37 x 3 + 12
We consider the new divisor 37 and the new remainder 12,and apply the division lemma to get
37 = 12 x 3 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 406 is 1
Notice that 1 = HCF(12,1) = HCF(37,12) = HCF(123,37) = HCF(283,123) = HCF(406,283) = HCF(689,406) .
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Frequently Asked Questions on HCF of 689, 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 689, 406?
Answer: HCF of 689, 406 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.