Highest Common Factor of 8328, 9906 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 8328, 9906 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 8328, 9906 is 6 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 8328, 9906 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 8328, 9906 is 6.
HCF(8328, 9906) = 6
HCF of 8328, 9906 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8328, 9906 is 6.
Highest Common Factor of 8328,9906 is 6
Step 1: Since 9906 > 8328, we apply the division lemma to 9906 and 8328, to get
9906 = 8328 x 1 + 1578
Step 2: Since the reminder 8328 ≠ 0, we apply division lemma to 1578 and 8328, to get
8328 = 1578 x 5 + 438
Step 3: We consider the new divisor 1578 and the new remainder 438, and apply the division lemma to get
1578 = 438 x 3 + 264
We consider the new divisor 438 and the new remainder 264,and apply the division lemma to get
438 = 264 x 1 + 174
We consider the new divisor 264 and the new remainder 174,and apply the division lemma to get
264 = 174 x 1 + 90
We consider the new divisor 174 and the new remainder 90,and apply the division lemma to get
174 = 90 x 1 + 84
We consider the new divisor 90 and the new remainder 84,and apply the division lemma to get
90 = 84 x 1 + 6
We consider the new divisor 84 and the new remainder 6,and apply the division lemma to get
84 = 6 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 8328 and 9906 is 6
Notice that 6 = HCF(84,6) = HCF(90,84) = HCF(174,90) = HCF(264,174) = HCF(438,264) = HCF(1578,438) = HCF(8328,1578) = HCF(9906,8328) .
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Frequently Asked Questions on HCF of 8328, 9906 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 8328, 9906?
Answer: HCF of 8328, 9906 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8328, 9906 using Euclid's Algorithm?
Answer: For arbitrary numbers 8328, 9906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
