Highest Common Factor of 320, 516, 282 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 320, 516, 282 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 320, 516, 282 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 320, 516, 282 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 320, 516, 282 is 2.
HCF(320, 516, 282) = 2
HCF of 320, 516, 282 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 320, 516, 282 is 2.
Highest Common Factor of 320,516,282 is 2
Step 1: Since 516 > 320, we apply the division lemma to 516 and 320, to get
516 = 320 x 1 + 196
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 196 and 320, to get
320 = 196 x 1 + 124
Step 3: We consider the new divisor 196 and the new remainder 124, and apply the division lemma to get
196 = 124 x 1 + 72
We consider the new divisor 124 and the new remainder 72,and apply the division lemma to get
124 = 72 x 1 + 52
We consider the new divisor 72 and the new remainder 52,and apply the division lemma to get
72 = 52 x 1 + 20
We consider the new divisor 52 and the new remainder 20,and apply the division lemma to get
52 = 20 x 2 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 320 and 516 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(52,20) = HCF(72,52) = HCF(124,72) = HCF(196,124) = HCF(320,196) = HCF(516,320) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 282 > 4, we apply the division lemma to 282 and 4, to get
282 = 4 x 70 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 282 is 2
Notice that 2 = HCF(4,2) = HCF(282,4) .
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Frequently Asked Questions on HCF of 320, 516, 282 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 320, 516, 282?
Answer: HCF of 320, 516, 282 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 320, 516, 282 using Euclid's Algorithm?
Answer: For arbitrary numbers 320, 516, 282 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.