Highest Common Factor of 85, 655, 823 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 85, 655, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 85, 655, 823 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 85, 655, 823 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 85, 655, 823 is 1.
HCF(85, 655, 823) = 1
HCF of 85, 655, 823 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 85, 655, 823 is 1.
Highest Common Factor of 85,655,823 is 1
Step 1: Since 655 > 85, we apply the division lemma to 655 and 85, to get
655 = 85 x 7 + 60
Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 60 and 85, to get
85 = 60 x 1 + 25
Step 3: We consider the new divisor 60 and the new remainder 25, and apply the division lemma to get
60 = 25 x 2 + 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 85 and 655 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(60,25) = HCF(85,60) = HCF(655,85) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 823 > 5, we apply the division lemma to 823 and 5, to get
823 = 5 x 164 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 823 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(823,5) .
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Frequently Asked Questions on HCF of 85, 655, 823 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 85, 655, 823?
Answer: HCF of 85, 655, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 85, 655, 823 using Euclid's Algorithm?
Answer: For arbitrary numbers 85, 655, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.