Highest Common Factor of 212, 66 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 212, 66 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 212, 66 is 2 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 212, 66 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 212, 66 is 2.
HCF(212, 66) = 2
HCF of 212, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 212, 66 is 2.
Highest Common Factor of 212,66 is 2
Step 1: Since 212 > 66, we apply the division lemma to 212 and 66, to get
212 = 66 x 3 + 14
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 14 and 66, to get
66 = 14 x 4 + 10
Step 3: We consider the new divisor 14 and the new remainder 10, and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 212 and 66 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) = HCF(212,66) .
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Frequently Asked Questions on HCF of 212, 66 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 212, 66?
Answer: HCF of 212, 66 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 212, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 212, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.