Highest Common Factor of 166, 214 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 166, 214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 166, 214 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 166, 214 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 166, 214 is 2.
HCF(166, 214) = 2
HCF of 166, 214 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 166, 214 is 2.
Highest Common Factor of 166,214 is 2
Step 1: Since 214 > 166, we apply the division lemma to 214 and 166, to get
214 = 166 x 1 + 48
Step 2: Since the reminder 166 ≠ 0, we apply division lemma to 48 and 166, to get
166 = 48 x 3 + 22
Step 3: We consider the new divisor 48 and the new remainder 22, and apply the division lemma to get
48 = 22 x 2 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 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 166 and 214 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(166,48) = HCF(214,166) .
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Frequently Asked Questions on HCF of 166, 214 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 166, 214?
Answer: HCF of 166, 214 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 166, 214 using Euclid's Algorithm?
Answer: For arbitrary numbers 166, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.