Highest Common Factor of 282, 458 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 282, 458 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 282, 458 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 282, 458 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 282, 458 is 2.
HCF(282, 458) = 2
HCF of 282, 458 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 282, 458 is 2.
Highest Common Factor of 282,458 is 2
Step 1: Since 458 > 282, we apply the division lemma to 458 and 282, to get
458 = 282 x 1 + 176
Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 176 and 282, to get
282 = 176 x 1 + 106
Step 3: We consider the new divisor 176 and the new remainder 106, and apply the division lemma to get
176 = 106 x 1 + 70
We consider the new divisor 106 and the new remainder 70,and apply the division lemma to get
106 = 70 x 1 + 36
We consider the new divisor 70 and the new remainder 36,and apply the division lemma to get
70 = 36 x 1 + 34
We consider the new divisor 36 and the new remainder 34,and apply the division lemma to get
36 = 34 x 1 + 2
We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 282 and 458 is 2
Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(70,36) = HCF(106,70) = HCF(176,106) = HCF(282,176) = HCF(458,282) .
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Frequently Asked Questions on HCF of 282, 458 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 282, 458?
Answer: HCF of 282, 458 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 282, 458 using Euclid's Algorithm?
Answer: For arbitrary numbers 282, 458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.