Highest Common Factor of 1643, 8704 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 1643, 8704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1643, 8704 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 1643, 8704 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 1643, 8704 is 1.
HCF(1643, 8704) = 1
HCF of 1643, 8704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1643, 8704 is 1.
Highest Common Factor of 1643,8704 is 1
Step 1: Since 8704 > 1643, we apply the division lemma to 8704 and 1643, to get
8704 = 1643 x 5 + 489
Step 2: Since the reminder 1643 ≠ 0, we apply division lemma to 489 and 1643, to get
1643 = 489 x 3 + 176
Step 3: We consider the new divisor 489 and the new remainder 176, and apply the division lemma to get
489 = 176 x 2 + 137
We consider the new divisor 176 and the new remainder 137,and apply the division lemma to get
176 = 137 x 1 + 39
We consider the new divisor 137 and the new remainder 39,and apply the division lemma to get
137 = 39 x 3 + 20
We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get
39 = 20 x 1 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1643 and 8704 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(137,39) = HCF(176,137) = HCF(489,176) = HCF(1643,489) = HCF(8704,1643) .
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Frequently Asked Questions on HCF of 1643, 8704 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 1643, 8704?
Answer: HCF of 1643, 8704 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1643, 8704 using Euclid's Algorithm?
Answer: For arbitrary numbers 1643, 8704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.