Highest Common Factor of 469, 646 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 469, 646 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 469, 646 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 469, 646 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 469, 646 is 1.
HCF(469, 646) = 1
HCF of 469, 646 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 469, 646 is 1.
Highest Common Factor of 469,646 is 1
Step 1: Since 646 > 469, we apply the division lemma to 646 and 469, to get
646 = 469 x 1 + 177
Step 2: Since the reminder 469 ≠ 0, we apply division lemma to 177 and 469, to get
469 = 177 x 2 + 115
Step 3: We consider the new divisor 177 and the new remainder 115, and apply the division lemma to get
177 = 115 x 1 + 62
We consider the new divisor 115 and the new remainder 62,and apply the division lemma to get
115 = 62 x 1 + 53
We consider the new divisor 62 and the new remainder 53,and apply the division lemma to get
62 = 53 x 1 + 9
We consider the new divisor 53 and the new remainder 9,and apply the division lemma to get
53 = 9 x 5 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 469 and 646 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(53,9) = HCF(62,53) = HCF(115,62) = HCF(177,115) = HCF(469,177) = HCF(646,469) .
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Frequently Asked Questions on HCF of 469, 646 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 469, 646?
Answer: HCF of 469, 646 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 469, 646 using Euclid's Algorithm?
Answer: For arbitrary numbers 469, 646 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
