Highest Common Factor of 9144, 6165 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 9144, 6165 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 9144, 6165 is 9 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 9144, 6165 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 9144, 6165 is 9.
HCF(9144, 6165) = 9
HCF of 9144, 6165 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9144, 6165 is 9.
Highest Common Factor of 9144,6165 is 9
Step 1: Since 9144 > 6165, we apply the division lemma to 9144 and 6165, to get
9144 = 6165 x 1 + 2979
Step 2: Since the reminder 6165 ≠ 0, we apply division lemma to 2979 and 6165, to get
6165 = 2979 x 2 + 207
Step 3: We consider the new divisor 2979 and the new remainder 207, and apply the division lemma to get
2979 = 207 x 14 + 81
We consider the new divisor 207 and the new remainder 81,and apply the division lemma to get
207 = 81 x 2 + 45
We consider the new divisor 81 and the new remainder 45,and apply the division lemma to get
81 = 45 x 1 + 36
We consider the new divisor 45 and the new remainder 36,and apply the division lemma to get
45 = 36 x 1 + 9
We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get
36 = 9 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9144 and 6165 is 9
Notice that 9 = HCF(36,9) = HCF(45,36) = HCF(81,45) = HCF(207,81) = HCF(2979,207) = HCF(6165,2979) = HCF(9144,6165) .
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Frequently Asked Questions on HCF of 9144, 6165 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 9144, 6165?
Answer: HCF of 9144, 6165 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9144, 6165 using Euclid's Algorithm?
Answer: For arbitrary numbers 9144, 6165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.