Highest Common Factor of 693, 83571 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 693, 83571 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 693, 83571 is 3 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 693, 83571 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 693, 83571 is 3.
HCF(693, 83571) = 3
HCF of 693, 83571 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 693, 83571 is 3.
Highest Common Factor of 693,83571 is 3
Step 1: Since 83571 > 693, we apply the division lemma to 83571 and 693, to get
83571 = 693 x 120 + 411
Step 2: Since the reminder 693 ≠ 0, we apply division lemma to 411 and 693, to get
693 = 411 x 1 + 282
Step 3: We consider the new divisor 411 and the new remainder 282, and apply the division lemma to get
411 = 282 x 1 + 129
We consider the new divisor 282 and the new remainder 129,and apply the division lemma to get
282 = 129 x 2 + 24
We consider the new divisor 129 and the new remainder 24,and apply the division lemma to get
129 = 24 x 5 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 693 and 83571 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(129,24) = HCF(282,129) = HCF(411,282) = HCF(693,411) = HCF(83571,693) .
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Frequently Asked Questions on HCF of 693, 83571 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 693, 83571?
Answer: HCF of 693, 83571 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 693, 83571 using Euclid's Algorithm?
Answer: For arbitrary numbers 693, 83571 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.