Highest Common Factor of 816, 306, 92 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, 306, 92 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 816, 306, 92 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, 306, 92 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, 306, 92 is 2.
HCF(816, 306, 92) = 2
HCF of 816, 306, 92 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, 306, 92 is 2.
Highest Common Factor of 816,306,92 is 2
Step 1: Since 816 > 306, we apply the division lemma to 816 and 306, to get
816 = 306 x 2 + 204
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 204 and 306, to get
306 = 204 x 1 + 102
Step 3: We consider the new divisor 204 and the new remainder 102, and apply the division lemma to get
204 = 102 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 102, the HCF of 816 and 306 is 102
Notice that 102 = HCF(204,102) = HCF(306,204) = HCF(816,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 92, we apply the division lemma to 102 and 92, to get
102 = 92 x 1 + 10
Step 2: Since the reminder 92 ≠ 0, we apply division lemma to 10 and 92, to get
92 = 10 x 9 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 102 and 92 is 2
Notice that 2 = HCF(10,2) = HCF(92,10) = HCF(102,92) .
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Frequently Asked Questions on HCF of 816, 306, 92 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, 306, 92?
Answer: HCF of 816, 306, 92 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 816, 306, 92 using Euclid's Algorithm?
Answer: For arbitrary numbers 816, 306, 92 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.