Highest Common Factor of 832, 306, 678 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 832, 306, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 832, 306, 678 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 832, 306, 678 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 832, 306, 678 is 2.
HCF(832, 306, 678) = 2
HCF of 832, 306, 678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 832, 306, 678 is 2.
Highest Common Factor of 832,306,678 is 2
Step 1: Since 832 > 306, we apply the division lemma to 832 and 306, to get
832 = 306 x 2 + 220
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 220 and 306, to get
306 = 220 x 1 + 86
Step 3: We consider the new divisor 220 and the new remainder 86, and apply the division lemma to get
220 = 86 x 2 + 48
We consider the new divisor 86 and the new remainder 48,and apply the division lemma to get
86 = 48 x 1 + 38
We consider the new divisor 48 and the new remainder 38,and apply the division lemma to get
48 = 38 x 1 + 10
We consider the new divisor 38 and the new remainder 10,and apply the division lemma to get
38 = 10 x 3 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 832 and 306 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(38,10) = HCF(48,38) = HCF(86,48) = HCF(220,86) = HCF(306,220) = HCF(832,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 2, we apply the division lemma to 678 and 2, to get
678 = 2 x 339 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 678 is 2
Notice that 2 = HCF(678,2) .
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Frequently Asked Questions on HCF of 832, 306, 678 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 832, 306, 678?
Answer: HCF of 832, 306, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 832, 306, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 832, 306, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.