Highest Common Factor of 312, 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 312, 822 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 822 is 6 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 312, 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 312, 822 is 6.
HCF(312, 822) = 6
HCF of 312, 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 312, 822 is 6.
Highest Common Factor of 312,822 is 6
Step 1: Since 822 > 312, we apply the division lemma to 822 and 312, to get
822 = 312 x 2 + 198
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 198 and 312, to get
312 = 198 x 1 + 114
Step 3: We consider the new divisor 198 and the new remainder 114, and apply the division lemma to get
198 = 114 x 1 + 84
We consider the new divisor 114 and the new remainder 84,and apply the division lemma to get
114 = 84 x 1 + 30
We consider the new divisor 84 and the new remainder 30,and apply the division lemma to get
84 = 30 x 2 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 312 and 822 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(84,30) = HCF(114,84) = HCF(198,114) = HCF(312,198) = HCF(822,312) .
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Frequently Asked Questions on HCF of 312, 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 312, 822?
Answer: HCF of 312, 822 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.