Highest Common Factor of 465, 8495, 3466 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 465, 8495, 3466 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 465, 8495, 3466 is 1 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 465, 8495, 3466 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 465, 8495, 3466 is 1.
HCF(465, 8495, 3466) = 1
HCF of 465, 8495, 3466 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 465, 8495, 3466 is 1.
Highest Common Factor of 465,8495,3466 is 1
Step 1: Since 8495 > 465, we apply the division lemma to 8495 and 465, to get
8495 = 465 x 18 + 125
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 125 and 465, to get
465 = 125 x 3 + 90
Step 3: We consider the new divisor 125 and the new remainder 90, and apply the division lemma to get
125 = 90 x 1 + 35
We consider the new divisor 90 and the new remainder 35,and apply the division lemma to get
90 = 35 x 2 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 465 and 8495 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(90,35) = HCF(125,90) = HCF(465,125) = HCF(8495,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3466 > 5, we apply the division lemma to 3466 and 5, to get
3466 = 5 x 693 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 3466 is 1
Notice that 1 = HCF(5,1) = HCF(3466,5) .
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Frequently Asked Questions on HCF of 465, 8495, 3466 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 465, 8495, 3466?
Answer: HCF of 465, 8495, 3466 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 465, 8495, 3466 using Euclid's Algorithm?
Answer: For arbitrary numbers 465, 8495, 3466 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.