Highest Common Factor of 474, 657, 996 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 474, 657, 996 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 657, 996 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 474, 657, 996 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 474, 657, 996 is 3.
HCF(474, 657, 996) = 3
HCF of 474, 657, 996 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 474, 657, 996 is 3.
Highest Common Factor of 474,657,996 is 3
Step 1: Since 657 > 474, we apply the division lemma to 657 and 474, to get
657 = 474 x 1 + 183
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 183 and 474, to get
474 = 183 x 2 + 108
Step 3: We consider the new divisor 183 and the new remainder 108, and apply the division lemma to get
183 = 108 x 1 + 75
We consider the new divisor 108 and the new remainder 75,and apply the division lemma to get
108 = 75 x 1 + 33
We consider the new divisor 75 and the new remainder 33,and apply the division lemma to get
75 = 33 x 2 + 9
We consider the new divisor 33 and the new remainder 9,and apply the division lemma to get
33 = 9 x 3 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 474 and 657 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(33,9) = HCF(75,33) = HCF(108,75) = HCF(183,108) = HCF(474,183) = HCF(657,474) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 996 > 3, we apply the division lemma to 996 and 3, to get
996 = 3 x 332 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 996 is 3
Notice that 3 = HCF(996,3) .
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Frequently Asked Questions on HCF of 474, 657, 996 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 474, 657, 996?
Answer: HCF of 474, 657, 996 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 657, 996 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 657, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.