Highest Common Factor of 561, 321, 301 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 561, 321, 301 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 561, 321, 301 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 561, 321, 301 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 561, 321, 301 is 1.
HCF(561, 321, 301) = 1
HCF of 561, 321, 301 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 561, 321, 301 is 1.
Highest Common Factor of 561,321,301 is 1
Step 1: Since 561 > 321, we apply the division lemma to 561 and 321, to get
561 = 321 x 1 + 240
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 240 and 321, to get
321 = 240 x 1 + 81
Step 3: We consider the new divisor 240 and the new remainder 81, and apply the division lemma to get
240 = 81 x 2 + 78
We consider the new divisor 81 and the new remainder 78,and apply the division lemma to get
81 = 78 x 1 + 3
We consider the new divisor 78 and the new remainder 3,and apply the division lemma to get
78 = 3 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 561 and 321 is 3
Notice that 3 = HCF(78,3) = HCF(81,78) = HCF(240,81) = HCF(321,240) = HCF(561,321) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 301 > 3, we apply the division lemma to 301 and 3, to get
301 = 3 x 100 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 301 is 1
Notice that 1 = HCF(3,1) = HCF(301,3) .
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Frequently Asked Questions on HCF of 561, 321, 301 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 561, 321, 301?
Answer: HCF of 561, 321, 301 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 561, 321, 301 using Euclid's Algorithm?
Answer: For arbitrary numbers 561, 321, 301 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.