Highest Common Factor of 458, 289 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, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 458, 289 is 1 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, 289 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, 289 is 1.
HCF(458, 289) = 1
HCF of 458, 289 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, 289 is 1.
Highest Common Factor of 458,289 is 1
Step 1: Since 458 > 289, we apply the division lemma to 458 and 289, to get
458 = 289 x 1 + 169
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 169 and 289, to get
289 = 169 x 1 + 120
Step 3: We consider the new divisor 169 and the new remainder 120, and apply the division lemma to get
169 = 120 x 1 + 49
We consider the new divisor 120 and the new remainder 49,and apply the division lemma to get
120 = 49 x 2 + 22
We consider the new divisor 49 and the new remainder 22,and apply the division lemma to get
49 = 22 x 2 + 5
We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get
22 = 5 x 4 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 458 and 289 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(49,22) = HCF(120,49) = HCF(169,120) = HCF(289,169) = HCF(458,289) .
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Frequently Asked Questions on HCF of 458, 289 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, 289?
Answer: HCF of 458, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 458, 289 using Euclid's Algorithm?
Answer: For arbitrary numbers 458, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.