Highest Common Factor of 221, 6712 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 221, 6712 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 221, 6712 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 221, 6712 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 221, 6712 is 1.
HCF(221, 6712) = 1
HCF of 221, 6712 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 221, 6712 is 1.
Highest Common Factor of 221,6712 is 1
Step 1: Since 6712 > 221, we apply the division lemma to 6712 and 221, to get
6712 = 221 x 30 + 82
Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 82 and 221, to get
221 = 82 x 2 + 57
Step 3: We consider the new divisor 82 and the new remainder 57, and apply the division lemma to get
82 = 57 x 1 + 25
We consider the new divisor 57 and the new remainder 25,and apply the division lemma to get
57 = 25 x 2 + 7
We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 221 and 6712 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(57,25) = HCF(82,57) = HCF(221,82) = HCF(6712,221) .
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Frequently Asked Questions on HCF of 221, 6712 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 221, 6712?
Answer: HCF of 221, 6712 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 221, 6712 using Euclid's Algorithm?
Answer: For arbitrary numbers 221, 6712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.