Highest Common Factor of 861, 237, 309 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 861, 237, 309 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 237, 309 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 861, 237, 309 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 861, 237, 309 is 3.
HCF(861, 237, 309) = 3
HCF of 861, 237, 309 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 861, 237, 309 is 3.
Highest Common Factor of 861,237,309 is 3
Step 1: Since 861 > 237, we apply the division lemma to 861 and 237, to get
861 = 237 x 3 + 150
Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 150 and 237, to get
237 = 150 x 1 + 87
Step 3: We consider the new divisor 150 and the new remainder 87, and apply the division lemma to get
150 = 87 x 1 + 63
We consider the new divisor 87 and the new remainder 63,and apply the division lemma to get
87 = 63 x 1 + 24
We consider the new divisor 63 and the new remainder 24,and apply the division lemma to get
63 = 24 x 2 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 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 861 and 237 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(63,24) = HCF(87,63) = HCF(150,87) = HCF(237,150) = HCF(861,237) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 3, we apply the division lemma to 309 and 3, to get
309 = 3 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 309 is 3
Notice that 3 = HCF(309,3) .
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Frequently Asked Questions on HCF of 861, 237, 309 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 861, 237, 309?
Answer: HCF of 861, 237, 309 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 237, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 237, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.