Highest Common Factor of 3165, 8991 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 3165, 8991 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3165, 8991 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 3165, 8991 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 3165, 8991 is 3.
HCF(3165, 8991) = 3
HCF of 3165, 8991 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3165, 8991 is 3.
Highest Common Factor of 3165,8991 is 3
Step 1: Since 8991 > 3165, we apply the division lemma to 8991 and 3165, to get
8991 = 3165 x 2 + 2661
Step 2: Since the reminder 3165 ≠ 0, we apply division lemma to 2661 and 3165, to get
3165 = 2661 x 1 + 504
Step 3: We consider the new divisor 2661 and the new remainder 504, and apply the division lemma to get
2661 = 504 x 5 + 141
We consider the new divisor 504 and the new remainder 141,and apply the division lemma to get
504 = 141 x 3 + 81
We consider the new divisor 141 and the new remainder 81,and apply the division lemma to get
141 = 81 x 1 + 60
We consider the new divisor 81 and the new remainder 60,and apply the division lemma to get
81 = 60 x 1 + 21
We consider the new divisor 60 and the new remainder 21,and apply the division lemma to get
60 = 21 x 2 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3165 and 8991 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(60,21) = HCF(81,60) = HCF(141,81) = HCF(504,141) = HCF(2661,504) = HCF(3165,2661) = HCF(8991,3165) .
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Frequently Asked Questions on HCF of 3165, 8991 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 3165, 8991?
Answer: HCF of 3165, 8991 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3165, 8991 using Euclid's Algorithm?
Answer: For arbitrary numbers 3165, 8991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.