Highest Common Factor of 1644, 6834, 86774 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 1644, 6834, 86774 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1644, 6834, 86774 is 2 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 1644, 6834, 86774 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 1644, 6834, 86774 is 2.
HCF(1644, 6834, 86774) = 2
HCF of 1644, 6834, 86774 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1644, 6834, 86774 is 2.
Highest Common Factor of 1644,6834,86774 is 2
Step 1: Since 6834 > 1644, we apply the division lemma to 6834 and 1644, to get
6834 = 1644 x 4 + 258
Step 2: Since the reminder 1644 ≠ 0, we apply division lemma to 258 and 1644, to get
1644 = 258 x 6 + 96
Step 3: We consider the new divisor 258 and the new remainder 96, and apply the division lemma to get
258 = 96 x 2 + 66
We consider the new divisor 96 and the new remainder 66,and apply the division lemma to get
96 = 66 x 1 + 30
We consider the new divisor 66 and the new remainder 30,and apply the division lemma to get
66 = 30 x 2 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1644 and 6834 is 6
Notice that 6 = HCF(30,6) = HCF(66,30) = HCF(96,66) = HCF(258,96) = HCF(1644,258) = HCF(6834,1644) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 86774 > 6, we apply the division lemma to 86774 and 6, to get
86774 = 6 x 14462 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 86774 is 2
Notice that 2 = HCF(6,2) = HCF(86774,6) .
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Frequently Asked Questions on HCF of 1644, 6834, 86774 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 1644, 6834, 86774?
Answer: HCF of 1644, 6834, 86774 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1644, 6834, 86774 using Euclid's Algorithm?
Answer: For arbitrary numbers 1644, 6834, 86774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
