Highest Common Factor of 9768, 585 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 9768, 585 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9768, 585 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 9768, 585 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 9768, 585 is 3.
HCF(9768, 585) = 3
HCF of 9768, 585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9768, 585 is 3.
Highest Common Factor of 9768,585 is 3
Step 1: Since 9768 > 585, we apply the division lemma to 9768 and 585, to get
9768 = 585 x 16 + 408
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 408 and 585, to get
585 = 408 x 1 + 177
Step 3: We consider the new divisor 408 and the new remainder 177, and apply the division lemma to get
408 = 177 x 2 + 54
We consider the new divisor 177 and the new remainder 54,and apply the division lemma to get
177 = 54 x 3 + 15
We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get
54 = 15 x 3 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 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 9768 and 585 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(177,54) = HCF(408,177) = HCF(585,408) = HCF(9768,585) .
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Frequently Asked Questions on HCF of 9768, 585 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 9768, 585?
Answer: HCF of 9768, 585 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9768, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 9768, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
