Highest Common Factor of 409, 9677, 6432 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 409, 9677, 6432 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 409, 9677, 6432 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 409, 9677, 6432 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 409, 9677, 6432 is 1.
HCF(409, 9677, 6432) = 1
HCF of 409, 9677, 6432 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 409, 9677, 6432 is 1.
Highest Common Factor of 409,9677,6432 is 1
Step 1: Since 9677 > 409, we apply the division lemma to 9677 and 409, to get
9677 = 409 x 23 + 270
Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 270 and 409, to get
409 = 270 x 1 + 139
Step 3: We consider the new divisor 270 and the new remainder 139, and apply the division lemma to get
270 = 139 x 1 + 131
We consider the new divisor 139 and the new remainder 131,and apply the division lemma to get
139 = 131 x 1 + 8
We consider the new divisor 131 and the new remainder 8,and apply the division lemma to get
131 = 8 x 16 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 9677 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(131,8) = HCF(139,131) = HCF(270,139) = HCF(409,270) = HCF(9677,409) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6432 > 1, we apply the division lemma to 6432 and 1, to get
6432 = 1 x 6432 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6432 is 1
Notice that 1 = HCF(6432,1) .
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Frequently Asked Questions on HCF of 409, 9677, 6432 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 409, 9677, 6432?
Answer: HCF of 409, 9677, 6432 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 409, 9677, 6432 using Euclid's Algorithm?
Answer: For arbitrary numbers 409, 9677, 6432 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.