Highest Common Factor of 676, 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 676, 406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 676, 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 676, 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 676, 406 is 2.
HCF(676, 406) = 2
HCF of 676, 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 676, 406 is 2.
Highest Common Factor of 676,406 is 2
Step 1: Since 676 > 406, we apply the division lemma to 676 and 406, to get
676 = 406 x 1 + 270
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 270 and 406, to get
406 = 270 x 1 + 136
Step 3: We consider the new divisor 270 and the new remainder 136, and apply the division lemma to get
270 = 136 x 1 + 134
We consider the new divisor 136 and the new remainder 134,and apply the division lemma to get
136 = 134 x 1 + 2
We consider the new divisor 134 and the new remainder 2,and apply the division lemma to get
134 = 2 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 676 and 406 is 2
Notice that 2 = HCF(134,2) = HCF(136,134) = HCF(270,136) = HCF(406,270) = HCF(676,406) .
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Frequently Asked Questions on HCF of 676, 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 676, 406?
Answer: HCF of 676, 406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 676, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 676, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.