Highest Common Factor of 182, 462, 166 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 182, 462, 166 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 182, 462, 166 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 182, 462, 166 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 182, 462, 166 is 2.
HCF(182, 462, 166) = 2
HCF of 182, 462, 166 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 182, 462, 166 is 2.
Highest Common Factor of 182,462,166 is 2
Step 1: Since 462 > 182, we apply the division lemma to 462 and 182, to get
462 = 182 x 2 + 98
Step 2: Since the reminder 182 ≠ 0, we apply division lemma to 98 and 182, to get
182 = 98 x 1 + 84
Step 3: We consider the new divisor 98 and the new remainder 84, and apply the division lemma to get
98 = 84 x 1 + 14
We consider the new divisor 84 and the new remainder 14, and apply the division lemma to get
84 = 14 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 182 and 462 is 14
Notice that 14 = HCF(84,14) = HCF(98,84) = HCF(182,98) = HCF(462,182) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 166 > 14, we apply the division lemma to 166 and 14, to get
166 = 14 x 11 + 12
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 12 and 14, to get
14 = 12 x 1 + 2
Step 3: 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 14 and 166 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(166,14) .
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Frequently Asked Questions on HCF of 182, 462, 166 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 182, 462, 166?
Answer: HCF of 182, 462, 166 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 182, 462, 166 using Euclid's Algorithm?
Answer: For arbitrary numbers 182, 462, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.