Highest Common Factor of 816, 186, 728 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 816, 186, 728 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 816, 186, 728 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 816, 186, 728 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 816, 186, 728 is 2.
HCF(816, 186, 728) = 2
HCF of 816, 186, 728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 816, 186, 728 is 2.
Highest Common Factor of 816,186,728 is 2
Step 1: Since 816 > 186, we apply the division lemma to 816 and 186, to get
816 = 186 x 4 + 72
Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 72 and 186, to get
186 = 72 x 2 + 42
Step 3: We consider the new divisor 72 and the new remainder 42, and apply the division lemma to get
72 = 42 x 1 + 30
We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get
42 = 30 x 1 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 816 and 186 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(72,42) = HCF(186,72) = HCF(816,186) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 728 > 6, we apply the division lemma to 728 and 6, to get
728 = 6 x 121 + 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 728 is 2
Notice that 2 = HCF(6,2) = HCF(728,6) .
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Frequently Asked Questions on HCF of 816, 186, 728 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 816, 186, 728?
Answer: HCF of 816, 186, 728 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 816, 186, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 816, 186, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.