Highest Common Factor of 9609, 8307 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 9609, 8307 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9609, 8307 is 3 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 9609, 8307 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 9609, 8307 is 3.
HCF(9609, 8307) = 3
HCF of 9609, 8307 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9609, 8307 is 3.
Highest Common Factor of 9609,8307 is 3
Step 1: Since 9609 > 8307, we apply the division lemma to 9609 and 8307, to get
9609 = 8307 x 1 + 1302
Step 2: Since the reminder 8307 ≠ 0, we apply division lemma to 1302 and 8307, to get
8307 = 1302 x 6 + 495
Step 3: We consider the new divisor 1302 and the new remainder 495, and apply the division lemma to get
1302 = 495 x 2 + 312
We consider the new divisor 495 and the new remainder 312,and apply the division lemma to get
495 = 312 x 1 + 183
We consider the new divisor 312 and the new remainder 183,and apply the division lemma to get
312 = 183 x 1 + 129
We consider the new divisor 183 and the new remainder 129,and apply the division lemma to get
183 = 129 x 1 + 54
We consider the new divisor 129 and the new remainder 54,and apply the division lemma to get
129 = 54 x 2 + 21
We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9609 and 8307 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(129,54) = HCF(183,129) = HCF(312,183) = HCF(495,312) = HCF(1302,495) = HCF(8307,1302) = HCF(9609,8307) .
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Frequently Asked Questions on HCF of 9609, 8307 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 9609, 8307?
Answer: HCF of 9609, 8307 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9609, 8307 using Euclid's Algorithm?
Answer: For arbitrary numbers 9609, 8307 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.