Highest Common Factor of 823, 180, 19 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 823, 180, 19 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 823, 180, 19 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 823, 180, 19 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 823, 180, 19 is 1.
HCF(823, 180, 19) = 1
HCF of 823, 180, 19 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 823, 180, 19 is 1.
Highest Common Factor of 823,180,19 is 1
Step 1: Since 823 > 180, we apply the division lemma to 823 and 180, to get
823 = 180 x 4 + 103
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 103 and 180, to get
180 = 103 x 1 + 77
Step 3: We consider the new divisor 103 and the new remainder 77, and apply the division lemma to get
103 = 77 x 1 + 26
We consider the new divisor 77 and the new remainder 26,and apply the division lemma to get
77 = 26 x 2 + 25
We consider the new divisor 26 and the new remainder 25,and apply the division lemma to get
26 = 25 x 1 + 1
We consider the new divisor 25 and the new remainder 1,and apply the division lemma to get
25 = 1 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 823 and 180 is 1
Notice that 1 = HCF(25,1) = HCF(26,25) = HCF(77,26) = HCF(103,77) = HCF(180,103) = HCF(823,180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 19 > 1, we apply the division lemma to 19 and 1, to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 19 is 1
Notice that 1 = HCF(19,1) .
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Frequently Asked Questions on HCF of 823, 180, 19 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 823, 180, 19?
Answer: HCF of 823, 180, 19 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 823, 180, 19 using Euclid's Algorithm?
Answer: For arbitrary numbers 823, 180, 19 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.