Highest Common Factor of 178, 199, 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 178, 199, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 178, 199, 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 178, 199, 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 178, 199, 823 is 1.
HCF(178, 199, 823) = 1
HCF of 178, 199, 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 178, 199, 823 is 1.
Highest Common Factor of 178,199,823 is 1
Step 1: Since 199 > 178, we apply the division lemma to 199 and 178, to get
199 = 178 x 1 + 21
Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 21 and 178, to get
178 = 21 x 8 + 10
Step 3: We consider the new divisor 21 and the new remainder 10, and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 178 and 199 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(178,21) = HCF(199,178) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 823 > 1, we apply the division lemma to 823 and 1, to get
823 = 1 x 823 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 823 is 1
Notice that 1 = HCF(823,1) .
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Frequently Asked Questions on HCF of 178, 199, 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 178, 199, 823?
Answer: HCF of 178, 199, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 178, 199, 823 using Euclid's Algorithm?
Answer: For arbitrary numbers 178, 199, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.