Highest Common Factor of 606, 819, 354 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 606, 819, 354 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 606, 819, 354 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 606, 819, 354 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 606, 819, 354 is 3.
HCF(606, 819, 354) = 3
HCF of 606, 819, 354 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 606, 819, 354 is 3.
Highest Common Factor of 606,819,354 is 3
Step 1: Since 819 > 606, we apply the division lemma to 819 and 606, to get
819 = 606 x 1 + 213
Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 213 and 606, to get
606 = 213 x 2 + 180
Step 3: We consider the new divisor 213 and the new remainder 180, and apply the division lemma to get
213 = 180 x 1 + 33
We consider the new divisor 180 and the new remainder 33,and apply the division lemma to get
180 = 33 x 5 + 15
We consider the new divisor 33 and the new remainder 15,and apply the division lemma to get
33 = 15 x 2 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 606 and 819 is 3
Notice that 3 = HCF(15,3) = HCF(33,15) = HCF(180,33) = HCF(213,180) = HCF(606,213) = HCF(819,606) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 354 > 3, we apply the division lemma to 354 and 3, to get
354 = 3 x 118 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 354 is 3
Notice that 3 = HCF(354,3) .
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Frequently Asked Questions on HCF of 606, 819, 354 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 606, 819, 354?
Answer: HCF of 606, 819, 354 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 606, 819, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 606, 819, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.