Highest Common Factor of 162, 267, 684 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 162, 267, 684 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 162, 267, 684 is 3 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 162, 267, 684 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 162, 267, 684 is 3.
HCF(162, 267, 684) = 3
HCF of 162, 267, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 162, 267, 684 is 3.
Highest Common Factor of 162,267,684 is 3
Step 1: Since 267 > 162, we apply the division lemma to 267 and 162, to get
267 = 162 x 1 + 105
Step 2: Since the reminder 162 ≠ 0, we apply division lemma to 105 and 162, to get
162 = 105 x 1 + 57
Step 3: We consider the new divisor 105 and the new remainder 57, and apply the division lemma to get
105 = 57 x 1 + 48
We consider the new divisor 57 and the new remainder 48,and apply the division lemma to get
57 = 48 x 1 + 9
We consider the new divisor 48 and the new remainder 9,and apply the division lemma to get
48 = 9 x 5 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 162 and 267 is 3
Notice that 3 = HCF(9,3) = HCF(48,9) = HCF(57,48) = HCF(105,57) = HCF(162,105) = HCF(267,162) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 684 > 3, we apply the division lemma to 684 and 3, to get
684 = 3 x 228 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 684 is 3
Notice that 3 = HCF(684,3) .
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Frequently Asked Questions on HCF of 162, 267, 684 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 162, 267, 684?
Answer: HCF of 162, 267, 684 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 162, 267, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 162, 267, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
