Highest Common Factor of 321, 559 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 321, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 321, 559 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 321, 559 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 321, 559 is 1.
HCF(321, 559) = 1
HCF of 321, 559 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 321, 559 is 1.
Highest Common Factor of 321,559 is 1
Step 1: Since 559 > 321, we apply the division lemma to 559 and 321, to get
559 = 321 x 1 + 238
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 238 and 321, to get
321 = 238 x 1 + 83
Step 3: We consider the new divisor 238 and the new remainder 83, and apply the division lemma to get
238 = 83 x 2 + 72
We consider the new divisor 83 and the new remainder 72,and apply the division lemma to get
83 = 72 x 1 + 11
We consider the new divisor 72 and the new remainder 11,and apply the division lemma to get
72 = 11 x 6 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 321 and 559 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(72,11) = HCF(83,72) = HCF(238,83) = HCF(321,238) = HCF(559,321) .
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Frequently Asked Questions on HCF of 321, 559 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 321, 559?
Answer: HCF of 321, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 321, 559 using Euclid's Algorithm?
Answer: For arbitrary numbers 321, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
