Highest Common Factor of 213, 8011, 3211 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 213, 8011, 3211 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 213, 8011, 3211 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 213, 8011, 3211 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 213, 8011, 3211 is 1.
HCF(213, 8011, 3211) = 1
HCF of 213, 8011, 3211 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 213, 8011, 3211 is 1.
Highest Common Factor of 213,8011,3211 is 1
Step 1: Since 8011 > 213, we apply the division lemma to 8011 and 213, to get
8011 = 213 x 37 + 130
Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 130 and 213, to get
213 = 130 x 1 + 83
Step 3: We consider the new divisor 130 and the new remainder 83, and apply the division lemma to get
130 = 83 x 1 + 47
We consider the new divisor 83 and the new remainder 47,and apply the division lemma to get
83 = 47 x 1 + 36
We consider the new divisor 47 and the new remainder 36,and apply the division lemma to get
47 = 36 x 1 + 11
We consider the new divisor 36 and the new remainder 11,and apply the division lemma to get
36 = 11 x 3 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 213 and 8011 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(36,11) = HCF(47,36) = HCF(83,47) = HCF(130,83) = HCF(213,130) = HCF(8011,213) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3211 > 1, we apply the division lemma to 3211 and 1, to get
3211 = 1 x 3211 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3211 is 1
Notice that 1 = HCF(3211,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 213, 8011, 3211 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 213, 8011, 3211?
Answer: HCF of 213, 8011, 3211 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 213, 8011, 3211 using Euclid's Algorithm?
Answer: For arbitrary numbers 213, 8011, 3211 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.