Highest Common Factor of 831, 469, 669 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 831, 469, 669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 831, 469, 669 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 831, 469, 669 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 831, 469, 669 is 1.
HCF(831, 469, 669) = 1
HCF of 831, 469, 669 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 831, 469, 669 is 1.
Highest Common Factor of 831,469,669 is 1
Step 1: Since 831 > 469, we apply the division lemma to 831 and 469, to get
831 = 469 x 1 + 362
Step 2: Since the reminder 469 ≠ 0, we apply division lemma to 362 and 469, to get
469 = 362 x 1 + 107
Step 3: We consider the new divisor 362 and the new remainder 107, and apply the division lemma to get
362 = 107 x 3 + 41
We consider the new divisor 107 and the new remainder 41,and apply the division lemma to get
107 = 41 x 2 + 25
We consider the new divisor 41 and the new remainder 25,and apply the division lemma to get
41 = 25 x 1 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 831 and 469 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(41,25) = HCF(107,41) = HCF(362,107) = HCF(469,362) = HCF(831,469) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 669 > 1, we apply the division lemma to 669 and 1, to get
669 = 1 x 669 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1
Notice that 1 = HCF(669,1) .
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Frequently Asked Questions on HCF of 831, 469, 669 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 831, 469, 669?
Answer: HCF of 831, 469, 669 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 831, 469, 669 using Euclid's Algorithm?
Answer: For arbitrary numbers 831, 469, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.