Highest Common Factor of 462, 312, 822, 500 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 462, 312, 822, 500 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 462, 312, 822, 500 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 462, 312, 822, 500 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 462, 312, 822, 500 is 2.
HCF(462, 312, 822, 500) = 2
HCF of 462, 312, 822, 500 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 462, 312, 822, 500 is 2.
Highest Common Factor of 462,312,822,500 is 2
Step 1: Since 462 > 312, we apply the division lemma to 462 and 312, to get
462 = 312 x 1 + 150
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 150 and 312, to get
312 = 150 x 2 + 12
Step 3: We consider the new divisor 150 and the new remainder 12, and apply the division lemma to get
150 = 12 x 12 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 462 and 312 is 6
Notice that 6 = HCF(12,6) = HCF(150,12) = HCF(312,150) = HCF(462,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 6, we apply the division lemma to 822 and 6, to get
822 = 6 x 137 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 822 is 6
Notice that 6 = HCF(822,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 500 > 6, we apply the division lemma to 500 and 6, to get
500 = 6 x 83 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 500 is 2
Notice that 2 = HCF(6,2) = HCF(500,6) .
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Frequently Asked Questions on HCF of 462, 312, 822, 500 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 462, 312, 822, 500?
Answer: HCF of 462, 312, 822, 500 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 462, 312, 822, 500 using Euclid's Algorithm?
Answer: For arbitrary numbers 462, 312, 822, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.