Highest Common Factor of 906, 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 906, 585 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 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 906, 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 906, 585 is 3.
HCF(906, 585) = 3
HCF of 906, 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 906, 585 is 3.
Highest Common Factor of 906,585 is 3
Step 1: Since 906 > 585, we apply the division lemma to 906 and 585, to get
906 = 585 x 1 + 321
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 321 and 585, to get
585 = 321 x 1 + 264
Step 3: We consider the new divisor 321 and the new remainder 264, and apply the division lemma to get
321 = 264 x 1 + 57
We consider the new divisor 264 and the new remainder 57,and apply the division lemma to get
264 = 57 x 4 + 36
We consider the new divisor 57 and the new remainder 36,and apply the division lemma to get
57 = 36 x 1 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 906 and 585 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(264,57) = HCF(321,264) = HCF(585,321) = HCF(906,585) .
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Frequently Asked Questions on HCF of 906, 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 906, 585?
Answer: HCF of 906, 585 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.