Highest Common Factor of 106, 172 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 106, 172 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 106, 172 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 106, 172 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 106, 172 is 2.
HCF(106, 172) = 2
HCF of 106, 172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 106, 172 is 2.
Highest Common Factor of 106,172 is 2
Step 1: Since 172 > 106, we apply the division lemma to 172 and 106, to get
172 = 106 x 1 + 66
Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 66 and 106, to get
106 = 66 x 1 + 40
Step 3: We consider the new divisor 66 and the new remainder 40, and apply the division lemma to get
66 = 40 x 1 + 26
We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get
40 = 26 x 1 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 106 and 172 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) = HCF(106,66) = HCF(172,106) .
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Frequently Asked Questions on HCF of 106, 172 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 106, 172?
Answer: HCF of 106, 172 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 106, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 106, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.