Highest Common Factor of 206, 741 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, 741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 206, 741 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 206, 741 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, 741 is 1.
HCF(206, 741) = 1
HCF of 206, 741 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, 741 is 1.
Highest Common Factor of 206,741 is 1
Step 1: Since 741 > 206, we apply the division lemma to 741 and 206, to get
741 = 206 x 3 + 123
Step 2: Since the reminder 206 ≠ 0, we apply division lemma to 123 and 206, to get
206 = 123 x 1 + 83
Step 3: We consider the new divisor 123 and the new remainder 83, and apply the division lemma to get
123 = 83 x 1 + 40
We consider the new divisor 83 and the new remainder 40,and apply the division lemma to get
83 = 40 x 2 + 3
We consider the new divisor 40 and the new remainder 3,and apply the division lemma to get
40 = 3 x 13 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 206 and 741 is 1
Notice that 1 = HCF(3,1) = HCF(40,3) = HCF(83,40) = HCF(123,83) = HCF(206,123) = HCF(741,206) .
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Frequently Asked Questions on HCF of 206, 741 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, 741?
Answer: HCF of 206, 741 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 206, 741 using Euclid's Algorithm?
Answer: For arbitrary numbers 206, 741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
