Highest Common Factor of 213, 971 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, 971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 213, 971 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, 971 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, 971 is 1.
HCF(213, 971) = 1
HCF of 213, 971 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, 971 is 1.
Highest Common Factor of 213,971 is 1
Step 1: Since 971 > 213, we apply the division lemma to 971 and 213, to get
971 = 213 x 4 + 119
Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 119 and 213, to get
213 = 119 x 1 + 94
Step 3: We consider the new divisor 119 and the new remainder 94, and apply the division lemma to get
119 = 94 x 1 + 25
We consider the new divisor 94 and the new remainder 25,and apply the division lemma to get
94 = 25 x 3 + 19
We consider the new divisor 25 and the new remainder 19,and apply the division lemma to get
25 = 19 x 1 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 213 and 971 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(25,19) = HCF(94,25) = HCF(119,94) = HCF(213,119) = HCF(971,213) .
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Frequently Asked Questions on HCF of 213, 971 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, 971?
Answer: HCF of 213, 971 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 213, 971 using Euclid's Algorithm?
Answer: For arbitrary numbers 213, 971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.