Highest Common Factor of 458, 7182 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 458, 7182 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 458, 7182 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 458, 7182 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 458, 7182 is 2.
HCF(458, 7182) = 2
HCF of 458, 7182 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 458, 7182 is 2.
Highest Common Factor of 458,7182 is 2
Step 1: Since 7182 > 458, we apply the division lemma to 7182 and 458, to get
7182 = 458 x 15 + 312
Step 2: Since the reminder 458 ≠ 0, we apply division lemma to 312 and 458, to get
458 = 312 x 1 + 146
Step 3: We consider the new divisor 312 and the new remainder 146, and apply the division lemma to get
312 = 146 x 2 + 20
We consider the new divisor 146 and the new remainder 20,and apply the division lemma to get
146 = 20 x 7 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma 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 458 and 7182 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(146,20) = HCF(312,146) = HCF(458,312) = HCF(7182,458) .
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Frequently Asked Questions on HCF of 458, 7182 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 458, 7182?
Answer: HCF of 458, 7182 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 458, 7182 using Euclid's Algorithm?
Answer: For arbitrary numbers 458, 7182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.