Highest Common Factor of 466, 978, 204 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, 978, 204 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 466, 978, 204 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 466, 978, 204 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, 978, 204 is 2.
HCF(466, 978, 204) = 2
HCF of 466, 978, 204 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, 978, 204 is 2.
Highest Common Factor of 466,978,204 is 2
Step 1: Since 978 > 466, we apply the division lemma to 978 and 466, to get
978 = 466 x 2 + 46
Step 2: Since the reminder 466 ≠ 0, we apply division lemma to 46 and 466, to get
466 = 46 x 10 + 6
Step 3: We consider the new divisor 46 and the new remainder 6, and apply the division lemma to get
46 = 6 x 7 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 466 and 978 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(46,6) = HCF(466,46) = HCF(978,466) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 204 > 2, we apply the division lemma to 204 and 2, to get
204 = 2 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 204 is 2
Notice that 2 = HCF(204,2) .
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Frequently Asked Questions on HCF of 466, 978, 204 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, 978, 204?
Answer: HCF of 466, 978, 204 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 466, 978, 204 using Euclid's Algorithm?
Answer: For arbitrary numbers 466, 978, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.