Highest Common Factor of 9735, 7453, 65159 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 9735, 7453, 65159 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9735, 7453, 65159 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 9735, 7453, 65159 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 9735, 7453, 65159 is 1.
HCF(9735, 7453, 65159) = 1
HCF of 9735, 7453, 65159 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9735, 7453, 65159 is 1.
Highest Common Factor of 9735,7453,65159 is 1
Step 1: Since 9735 > 7453, we apply the division lemma to 9735 and 7453, to get
9735 = 7453 x 1 + 2282
Step 2: Since the reminder 7453 ≠ 0, we apply division lemma to 2282 and 7453, to get
7453 = 2282 x 3 + 607
Step 3: We consider the new divisor 2282 and the new remainder 607, and apply the division lemma to get
2282 = 607 x 3 + 461
We consider the new divisor 607 and the new remainder 461,and apply the division lemma to get
607 = 461 x 1 + 146
We consider the new divisor 461 and the new remainder 146,and apply the division lemma to get
461 = 146 x 3 + 23
We consider the new divisor 146 and the new remainder 23,and apply the division lemma to get
146 = 23 x 6 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9735 and 7453 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(146,23) = HCF(461,146) = HCF(607,461) = HCF(2282,607) = HCF(7453,2282) = HCF(9735,7453) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65159 > 1, we apply the division lemma to 65159 and 1, to get
65159 = 1 x 65159 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65159 is 1
Notice that 1 = HCF(65159,1) .
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Frequently Asked Questions on HCF of 9735, 7453, 65159 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 9735, 7453, 65159?
Answer: HCF of 9735, 7453, 65159 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9735, 7453, 65159 using Euclid's Algorithm?
Answer: For arbitrary numbers 9735, 7453, 65159 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.