Highest Common Factor of 87, 309, 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 87, 309, 606 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 87, 309, 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 87, 309, 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 87, 309, 606 is 3.
HCF(87, 309, 606) = 3
HCF of 87, 309, 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 87, 309, 606 is 3.
Highest Common Factor of 87,309,606 is 3
Step 1: Since 309 > 87, we apply the division lemma to 309 and 87, to get
309 = 87 x 3 + 48
Step 2: Since the reminder 87 ≠ 0, we apply division lemma to 48 and 87, to get
87 = 48 x 1 + 39
Step 3: We consider the new divisor 48 and the new remainder 39, and apply the division lemma to get
48 = 39 x 1 + 9
We consider the new divisor 39 and the new remainder 9,and apply the division lemma to get
39 = 9 x 4 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 87 and 309 is 3
Notice that 3 = HCF(9,3) = HCF(39,9) = HCF(48,39) = HCF(87,48) = HCF(309,87) .
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 87, 309, 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 87, 309, 606?
Answer: HCF of 87, 309, 606 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 87, 309, 606 using Euclid's Algorithm?
Answer: For arbitrary numbers 87, 309, 606 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.