Highest Common Factor of 8906, 9834 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 8906, 9834 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8906, 9834 is 2 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 8906, 9834 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 8906, 9834 is 2.
HCF(8906, 9834) = 2
HCF of 8906, 9834 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8906, 9834 is 2.
Highest Common Factor of 8906,9834 is 2
Step 1: Since 9834 > 8906, we apply the division lemma to 9834 and 8906, to get
9834 = 8906 x 1 + 928
Step 2: Since the reminder 8906 ≠ 0, we apply division lemma to 928 and 8906, to get
8906 = 928 x 9 + 554
Step 3: We consider the new divisor 928 and the new remainder 554, and apply the division lemma to get
928 = 554 x 1 + 374
We consider the new divisor 554 and the new remainder 374,and apply the division lemma to get
554 = 374 x 1 + 180
We consider the new divisor 374 and the new remainder 180,and apply the division lemma to get
374 = 180 x 2 + 14
We consider the new divisor 180 and the new remainder 14,and apply the division lemma to get
180 = 14 x 12 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8906 and 9834 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(180,14) = HCF(374,180) = HCF(554,374) = HCF(928,554) = HCF(8906,928) = HCF(9834,8906) .
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Frequently Asked Questions on HCF of 8906, 9834 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 8906, 9834?
Answer: HCF of 8906, 9834 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8906, 9834 using Euclid's Algorithm?
Answer: For arbitrary numbers 8906, 9834 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.