Highest Common Factor of 459, 359 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 459, 359 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 359 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 459, 359 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 459, 359 is 1.
HCF(459, 359) = 1
HCF of 459, 359 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 359 is 1.
Highest Common Factor of 459,359 is 1
Step 1: Since 459 > 359, we apply the division lemma to 459 and 359, to get
459 = 359 x 1 + 100
Step 2: Since the reminder 359 ≠ 0, we apply division lemma to 100 and 359, to get
359 = 100 x 3 + 59
Step 3: We consider the new divisor 100 and the new remainder 59, and apply the division lemma to get
100 = 59 x 1 + 41
We consider the new divisor 59 and the new remainder 41,and apply the division lemma to get
59 = 41 x 1 + 18
We consider the new divisor 41 and the new remainder 18,and apply the division lemma to get
41 = 18 x 2 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 459 and 359 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(41,18) = HCF(59,41) = HCF(100,59) = HCF(359,100) = HCF(459,359) .
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Frequently Asked Questions on HCF of 459, 359 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 459, 359?
Answer: HCF of 459, 359 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 359 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 359 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.