Highest Common Factor of 466, 2670, 4163 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 466, 2670, 4163 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 466, 2670, 4163 is 1 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 466, 2670, 4163 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 466, 2670, 4163 is 1.
HCF(466, 2670, 4163) = 1
HCF of 466, 2670, 4163 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 466, 2670, 4163 is 1.
Highest Common Factor of 466,2670,4163 is 1
Step 1: Since 2670 > 466, we apply the division lemma to 2670 and 466, to get
2670 = 466 x 5 + 340
Step 2: Since the reminder 466 ≠ 0, we apply division lemma to 340 and 466, to get
466 = 340 x 1 + 126
Step 3: We consider the new divisor 340 and the new remainder 126, and apply the division lemma to get
340 = 126 x 2 + 88
We consider the new divisor 126 and the new remainder 88,and apply the division lemma to get
126 = 88 x 1 + 38
We consider the new divisor 88 and the new remainder 38,and apply the division lemma to get
88 = 38 x 2 + 12
We consider the new divisor 38 and the new remainder 12,and apply the division lemma to get
38 = 12 x 3 + 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 466 and 2670 is 2
Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(88,38) = HCF(126,88) = HCF(340,126) = HCF(466,340) = HCF(2670,466) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4163 > 2, we apply the division lemma to 4163 and 2, to get
4163 = 2 x 2081 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 4163 is 1
Notice that 1 = HCF(2,1) = HCF(4163,2) .
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Frequently Asked Questions on HCF of 466, 2670, 4163 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 466, 2670, 4163?
Answer: HCF of 466, 2670, 4163 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 466, 2670, 4163 using Euclid's Algorithm?
Answer: For arbitrary numbers 466, 2670, 4163 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
