Highest Common Factor of 547, 9704 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 547, 9704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 547, 9704 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 547, 9704 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 547, 9704 is 1.
HCF(547, 9704) = 1
HCF of 547, 9704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 547, 9704 is 1.
Highest Common Factor of 547,9704 is 1
Step 1: Since 9704 > 547, we apply the division lemma to 9704 and 547, to get
9704 = 547 x 17 + 405
Step 2: Since the reminder 547 ≠ 0, we apply division lemma to 405 and 547, to get
547 = 405 x 1 + 142
Step 3: We consider the new divisor 405 and the new remainder 142, and apply the division lemma to get
405 = 142 x 2 + 121
We consider the new divisor 142 and the new remainder 121,and apply the division lemma to get
142 = 121 x 1 + 21
We consider the new divisor 121 and the new remainder 21,and apply the division lemma to get
121 = 21 x 5 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 547 and 9704 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(121,21) = HCF(142,121) = HCF(405,142) = HCF(547,405) = HCF(9704,547) .
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Frequently Asked Questions on HCF of 547, 9704 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 547, 9704?
Answer: HCF of 547, 9704 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 547, 9704 using Euclid's Algorithm?
Answer: For arbitrary numbers 547, 9704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.