Highest Common Factor of 822, 742, 366 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 822, 742, 366 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 742, 366 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 822, 742, 366 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 822, 742, 366 is 2.
HCF(822, 742, 366) = 2
HCF of 822, 742, 366 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 742, 366 is 2.
Highest Common Factor of 822,742,366 is 2
Step 1: Since 822 > 742, we apply the division lemma to 822 and 742, to get
822 = 742 x 1 + 80
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 80 and 742, to get
742 = 80 x 9 + 22
Step 3: We consider the new divisor 80 and the new remainder 22, and apply the division lemma to get
80 = 22 x 3 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma 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 822 and 742 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(80,22) = HCF(742,80) = HCF(822,742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 366 > 2, we apply the division lemma to 366 and 2, to get
366 = 2 x 183 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 366 is 2
Notice that 2 = HCF(366,2) .
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Frequently Asked Questions on HCF of 822, 742, 366 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 822, 742, 366?
Answer: HCF of 822, 742, 366 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 742, 366 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 742, 366 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.