Highest Common Factor of 330, 782, 822 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 330, 782, 822 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 330, 782, 822 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 330, 782, 822 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 330, 782, 822 is 2.
HCF(330, 782, 822) = 2
HCF of 330, 782, 822 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 330, 782, 822 is 2.
Highest Common Factor of 330,782,822 is 2
Step 1: Since 782 > 330, we apply the division lemma to 782 and 330, to get
782 = 330 x 2 + 122
Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 122 and 330, to get
330 = 122 x 2 + 86
Step 3: We consider the new divisor 122 and the new remainder 86, and apply the division lemma to get
122 = 86 x 1 + 36
We consider the new divisor 86 and the new remainder 36,and apply the division lemma to get
86 = 36 x 2 + 14
We consider the new divisor 36 and the new remainder 14,and apply the division lemma to get
36 = 14 x 2 + 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 330 and 782 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(36,14) = HCF(86,36) = HCF(122,86) = HCF(330,122) = HCF(782,330) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 2, we apply the division lemma to 822 and 2, to get
822 = 2 x 411 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 822 is 2
Notice that 2 = HCF(822,2) .
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Frequently Asked Questions on HCF of 330, 782, 822 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 330, 782, 822?
Answer: HCF of 330, 782, 822 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 330, 782, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 330, 782, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.