Highest Common Factor of 165, 5398 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 165, 5398 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 165, 5398 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 165, 5398 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 165, 5398 is 1.
HCF(165, 5398) = 1
HCF of 165, 5398 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 165, 5398 is 1.
Highest Common Factor of 165,5398 is 1
Step 1: Since 5398 > 165, we apply the division lemma to 5398 and 165, to get
5398 = 165 x 32 + 118
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 118 and 165, to get
165 = 118 x 1 + 47
Step 3: We consider the new divisor 118 and the new remainder 47, and apply the division lemma to get
118 = 47 x 2 + 24
We consider the new divisor 47 and the new remainder 24,and apply the division lemma to get
47 = 24 x 1 + 23
We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get
24 = 23 x 1 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 165 and 5398 is 1
Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(47,24) = HCF(118,47) = HCF(165,118) = HCF(5398,165) .
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Frequently Asked Questions on HCF of 165, 5398 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 165, 5398?
Answer: HCF of 165, 5398 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 165, 5398 using Euclid's Algorithm?
Answer: For arbitrary numbers 165, 5398 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.