Highest Common Factor of 585, 162, 231 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 585, 162, 231 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 162, 231 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 585, 162, 231 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 585, 162, 231 is 3.
HCF(585, 162, 231) = 3
HCF of 585, 162, 231 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 585, 162, 231 is 3.
Highest Common Factor of 585,162,231 is 3
Step 1: Since 585 > 162, we apply the division lemma to 585 and 162, to get
585 = 162 x 3 + 99
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 99 and 162, to get
162 = 99 x 1 + 63
Step 3: We consider the new divisor 99 and the new remainder 63, and apply the division lemma to get
99 = 63 x 1 + 36
We consider the new divisor 63 and the new remainder 36,and apply the division lemma to get
63 = 36 x 1 + 27
We consider the new divisor 36 and the new remainder 27,and apply the division lemma to get
36 = 27 x 1 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 585 and 162 is 9
Notice that 9 = HCF(27,9) = HCF(36,27) = HCF(63,36) = HCF(99,63) = HCF(162,99) = HCF(585,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 231 > 9, we apply the division lemma to 231 and 9, to get
231 = 9 x 25 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 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 9 and 231 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(231,9) .
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Frequently Asked Questions on HCF of 585, 162, 231 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 585, 162, 231?
Answer: HCF of 585, 162, 231 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 162, 231 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 162, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.