Highest Common Factor of 212, 460, 162 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, 460, 162 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 212, 460, 162 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, 460, 162 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, 460, 162 is 2.
HCF(212, 460, 162) = 2
HCF of 212, 460, 162 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, 460, 162 is 2.
Highest Common Factor of 212,460,162 is 2
Step 1: Since 460 > 212, we apply the division lemma to 460 and 212, to get
460 = 212 x 2 + 36
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 36 and 212, to get
212 = 36 x 5 + 32
Step 3: We consider the new divisor 36 and the new remainder 32, and apply the division lemma to get
36 = 32 x 1 + 4
We consider the new divisor 32 and the new remainder 4, and apply the division lemma to get
32 = 4 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 212 and 460 is 4
Notice that 4 = HCF(32,4) = HCF(36,32) = HCF(212,36) = HCF(460,212) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 162 > 4, we apply the division lemma to 162 and 4, to get
162 = 4 x 40 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 162 is 2
Notice that 2 = HCF(4,2) = HCF(162,4) .
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Frequently Asked Questions on HCF of 212, 460, 162 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, 460, 162?
Answer: HCF of 212, 460, 162 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 212, 460, 162 using Euclid's Algorithm?
Answer: For arbitrary numbers 212, 460, 162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.