Highest Common Factor of 206, 178 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 206, 178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 206, 178 is 2 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 206, 178 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 206, 178 is 2.
HCF(206, 178) = 2
HCF of 206, 178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 206, 178 is 2.
Highest Common Factor of 206,178 is 2
Step 1: Since 206 > 178, we apply the division lemma to 206 and 178, to get
206 = 178 x 1 + 28
Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 28 and 178, to get
178 = 28 x 6 + 10
Step 3: We consider the new divisor 28 and the new remainder 10, and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 206 and 178 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(178,28) = HCF(206,178) .
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Frequently Asked Questions on HCF of 206, 178 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 206, 178?
Answer: HCF of 206, 178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 206, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 206, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.