Highest Common Factor of 71, 90, 55, 206 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 71, 90, 55, 206 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 71, 90, 55, 206 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 71, 90, 55, 206 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 71, 90, 55, 206 is 1.
HCF(71, 90, 55, 206) = 1
HCF of 71, 90, 55, 206 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 71, 90, 55, 206 is 1.
Highest Common Factor of 71,90,55,206 is 1
Step 1: Since 90 > 71, we apply the division lemma to 90 and 71, to get
90 = 71 x 1 + 19
Step 2: Since the reminder 71 ≠ 0, we apply division lemma to 19 and 71, to get
71 = 19 x 3 + 14
Step 3: We consider the new divisor 19 and the new remainder 14, and apply the division lemma to get
19 = 14 x 1 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 71 and 90 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(71,19) = HCF(90,71) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 1, we apply the division lemma to 55 and 1, to get
55 = 1 x 55 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 55 is 1
Notice that 1 = HCF(55,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 206 > 1, we apply the division lemma to 206 and 1, to get
206 = 1 x 206 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 206 is 1
Notice that 1 = HCF(206,1) .
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Frequently Asked Questions on HCF of 71, 90, 55, 206 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 71, 90, 55, 206?
Answer: HCF of 71, 90, 55, 206 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 71, 90, 55, 206 using Euclid's Algorithm?
Answer: For arbitrary numbers 71, 90, 55, 206 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
