Highest Common Factor of 909, 345, 606 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 909, 345, 606 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 345, 606 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 909, 345, 606 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 909, 345, 606 is 3.
HCF(909, 345, 606) = 3
HCF of 909, 345, 606 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 909, 345, 606 is 3.
Highest Common Factor of 909,345,606 is 3
Step 1: Since 909 > 345, we apply the division lemma to 909 and 345, to get
909 = 345 x 2 + 219
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 219 and 345, to get
345 = 219 x 1 + 126
Step 3: We consider the new divisor 219 and the new remainder 126, and apply the division lemma to get
219 = 126 x 1 + 93
We consider the new divisor 126 and the new remainder 93,and apply the division lemma to get
126 = 93 x 1 + 33
We consider the new divisor 93 and the new remainder 33,and apply the division lemma to get
93 = 33 x 2 + 27
We consider the new divisor 33 and the new remainder 27,and apply the division lemma to get
33 = 27 x 1 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 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 909 and 345 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(93,33) = HCF(126,93) = HCF(219,126) = HCF(345,219) = HCF(909,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 606 > 3, we apply the division lemma to 606 and 3, to get
606 = 3 x 202 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 606 is 3
Notice that 3 = HCF(606,3) .
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Frequently Asked Questions on HCF of 909, 345, 606 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 909, 345, 606?
Answer: HCF of 909, 345, 606 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 345, 606 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 345, 606 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.