Highest Common Factor of 8629, 9000 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 8629, 9000 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8629, 9000 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 8629, 9000 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 8629, 9000 is 1.
HCF(8629, 9000) = 1
HCF of 8629, 9000 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8629, 9000 is 1.
Highest Common Factor of 8629,9000 is 1
Step 1: Since 9000 > 8629, we apply the division lemma to 9000 and 8629, to get
9000 = 8629 x 1 + 371
Step 2: Since the reminder 8629 ≠ 0, we apply division lemma to 371 and 8629, to get
8629 = 371 x 23 + 96
Step 3: We consider the new divisor 371 and the new remainder 96, and apply the division lemma to get
371 = 96 x 3 + 83
We consider the new divisor 96 and the new remainder 83,and apply the division lemma to get
96 = 83 x 1 + 13
We consider the new divisor 83 and the new remainder 13,and apply the division lemma to get
83 = 13 x 6 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8629 and 9000 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(83,13) = HCF(96,83) = HCF(371,96) = HCF(8629,371) = HCF(9000,8629) .
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Frequently Asked Questions on HCF of 8629, 9000 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 8629, 9000?
Answer: HCF of 8629, 9000 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8629, 9000 using Euclid's Algorithm?
Answer: For arbitrary numbers 8629, 9000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
