Highest Common Factor of 1585, 8591 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 1585, 8591 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1585, 8591 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 1585, 8591 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 1585, 8591 is 1.
HCF(1585, 8591) = 1
HCF of 1585, 8591 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1585, 8591 is 1.
Highest Common Factor of 1585,8591 is 1
Step 1: Since 8591 > 1585, we apply the division lemma to 8591 and 1585, to get
8591 = 1585 x 5 + 666
Step 2: Since the reminder 1585 ≠ 0, we apply division lemma to 666 and 1585, to get
1585 = 666 x 2 + 253
Step 3: We consider the new divisor 666 and the new remainder 253, and apply the division lemma to get
666 = 253 x 2 + 160
We consider the new divisor 253 and the new remainder 160,and apply the division lemma to get
253 = 160 x 1 + 93
We consider the new divisor 160 and the new remainder 93,and apply the division lemma to get
160 = 93 x 1 + 67
We consider the new divisor 93 and the new remainder 67,and apply the division lemma to get
93 = 67 x 1 + 26
We consider the new divisor 67 and the new remainder 26,and apply the division lemma to get
67 = 26 x 2 + 15
We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get
26 = 15 x 1 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1585 and 8591 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(67,26) = HCF(93,67) = HCF(160,93) = HCF(253,160) = HCF(666,253) = HCF(1585,666) = HCF(8591,1585) .
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Frequently Asked Questions on HCF of 1585, 8591 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 1585, 8591?
Answer: HCF of 1585, 8591 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1585, 8591 using Euclid's Algorithm?
Answer: For arbitrary numbers 1585, 8591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.