Highest Common Factor of 405, 965, 85 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 405, 965, 85 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 965, 85 is 5 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 405, 965, 85 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 405, 965, 85 is 5.
HCF(405, 965, 85) = 5
HCF of 405, 965, 85 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 965, 85 is 5.
Highest Common Factor of 405,965,85 is 5
Step 1: Since 965 > 405, we apply the division lemma to 965 and 405, to get
965 = 405 x 2 + 155
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 155 and 405, to get
405 = 155 x 2 + 95
Step 3: We consider the new divisor 155 and the new remainder 95, and apply the division lemma to get
155 = 95 x 1 + 60
We consider the new divisor 95 and the new remainder 60,and apply the division lemma to get
95 = 60 x 1 + 35
We consider the new divisor 60 and the new remainder 35,and apply the division lemma to get
60 = 35 x 1 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 405 and 965 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) = HCF(95,60) = HCF(155,95) = HCF(405,155) = HCF(965,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85 > 5, we apply the division lemma to 85 and 5, to get
85 = 5 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 85 is 5
Notice that 5 = HCF(85,5) .
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Frequently Asked Questions on HCF of 405, 965, 85 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 405, 965, 85?
Answer: HCF of 405, 965, 85 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 965, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 965, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.