Highest Common Factor of 589, 8006 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 589, 8006 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 589, 8006 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 589, 8006 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 589, 8006 is 1.
HCF(589, 8006) = 1
HCF of 589, 8006 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 589, 8006 is 1.
Highest Common Factor of 589,8006 is 1
Step 1: Since 8006 > 589, we apply the division lemma to 8006 and 589, to get
8006 = 589 x 13 + 349
Step 2: Since the reminder 589 ≠ 0, we apply division lemma to 349 and 589, to get
589 = 349 x 1 + 240
Step 3: We consider the new divisor 349 and the new remainder 240, and apply the division lemma to get
349 = 240 x 1 + 109
We consider the new divisor 240 and the new remainder 109,and apply the division lemma to get
240 = 109 x 2 + 22
We consider the new divisor 109 and the new remainder 22,and apply the division lemma to get
109 = 22 x 4 + 21
We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get
22 = 21 x 1 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 589 and 8006 is 1
Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(109,22) = HCF(240,109) = HCF(349,240) = HCF(589,349) = HCF(8006,589) .
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Frequently Asked Questions on HCF of 589, 8006 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 589, 8006?
Answer: HCF of 589, 8006 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 589, 8006 using Euclid's Algorithm?
Answer: For arbitrary numbers 589, 8006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.