Highest Common Factor of 678, 861, 846, 29 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 678, 861, 846, 29 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 861, 846, 29 is 1 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 678, 861, 846, 29 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 678, 861, 846, 29 is 1.
HCF(678, 861, 846, 29) = 1
HCF of 678, 861, 846, 29 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 861, 846, 29 is 1.
Highest Common Factor of 678,861,846,29 is 1
Step 1: Since 861 > 678, we apply the division lemma to 861 and 678, to get
861 = 678 x 1 + 183
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 183 and 678, to get
678 = 183 x 3 + 129
Step 3: We consider the new divisor 183 and the new remainder 129, and apply the division lemma to get
183 = 129 x 1 + 54
We consider the new divisor 129 and the new remainder 54,and apply the division lemma to get
129 = 54 x 2 + 21
We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 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 678 and 861 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(129,54) = HCF(183,129) = HCF(678,183) = HCF(861,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 846 > 3, we apply the division lemma to 846 and 3, to get
846 = 3 x 282 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 846 is 3
Notice that 3 = HCF(846,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 29 > 3, we apply the division lemma to 29 and 3, to get
29 = 3 x 9 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 29 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(29,3) .
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Frequently Asked Questions on HCF of 678, 861, 846, 29 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 678, 861, 846, 29?
Answer: HCF of 678, 861, 846, 29 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 861, 846, 29 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 861, 846, 29 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
