Highest Common Factor of 582, 702, 816 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 582, 702, 816 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 702, 816 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 582, 702, 816 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 582, 702, 816 is 6.
HCF(582, 702, 816) = 6
HCF of 582, 702, 816 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 582, 702, 816 is 6.
Highest Common Factor of 582,702,816 is 6
Step 1: Since 702 > 582, we apply the division lemma to 702 and 582, to get
702 = 582 x 1 + 120
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 120 and 582, to get
582 = 120 x 4 + 102
Step 3: We consider the new divisor 120 and the new remainder 102, and apply the division lemma to get
120 = 102 x 1 + 18
We consider the new divisor 102 and the new remainder 18,and apply the division lemma to get
102 = 18 x 5 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 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 582 and 702 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(102,18) = HCF(120,102) = HCF(582,120) = HCF(702,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 816 > 6, we apply the division lemma to 816 and 6, to get
816 = 6 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 816 is 6
Notice that 6 = HCF(816,6) .
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Frequently Asked Questions on HCF of 582, 702, 816 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 582, 702, 816?
Answer: HCF of 582, 702, 816 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 702, 816 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 702, 816 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.