Highest Common Factor of 309, 846, 861 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 309, 846, 861 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 846, 861 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 309, 846, 861 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 309, 846, 861 is 3.
HCF(309, 846, 861) = 3
HCF of 309, 846, 861 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 846, 861 is 3.
Highest Common Factor of 309,846,861 is 3
Step 1: Since 846 > 309, we apply the division lemma to 846 and 309, to get
846 = 309 x 2 + 228
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 228 and 309, to get
309 = 228 x 1 + 81
Step 3: We consider the new divisor 228 and the new remainder 81, and apply the division lemma to get
228 = 81 x 2 + 66
We consider the new divisor 81 and the new remainder 66,and apply the division lemma to get
81 = 66 x 1 + 15
We consider the new divisor 66 and the new remainder 15,and apply the division lemma to get
66 = 15 x 4 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 309 and 846 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(66,15) = HCF(81,66) = HCF(228,81) = HCF(309,228) = HCF(846,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 861 > 3, we apply the division lemma to 861 and 3, to get
861 = 3 x 287 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 861 is 3
Notice that 3 = HCF(861,3) .
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Frequently Asked Questions on HCF of 309, 846, 861 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 309, 846, 861?
Answer: HCF of 309, 846, 861 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 846, 861 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 846, 861 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.