Highest Common Factor of 496, 217, 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 496, 217, 822 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 496, 217, 822 is 1 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 496, 217, 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 496, 217, 822 is 1.
HCF(496, 217, 822) = 1
HCF of 496, 217, 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 496, 217, 822 is 1.
Highest Common Factor of 496,217,822 is 1
Step 1: Since 496 > 217, we apply the division lemma to 496 and 217, to get
496 = 217 x 2 + 62
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 62 and 217, to get
217 = 62 x 3 + 31
Step 3: We consider the new divisor 62 and the new remainder 31, and apply the division lemma to get
62 = 31 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 496 and 217 is 31
Notice that 31 = HCF(62,31) = HCF(217,62) = HCF(496,217) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 31, we apply the division lemma to 822 and 31, to get
822 = 31 x 26 + 16
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 16 and 31, to get
31 = 16 x 1 + 15
Step 3: We consider the new divisor 16 and the new remainder 15, and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1, and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 31 and 822 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(31,16) = HCF(822,31) .
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Frequently Asked Questions on HCF of 496, 217, 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 496, 217, 822?
Answer: HCF of 496, 217, 822 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 496, 217, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 496, 217, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.