Highest Common Factor of 521, 362, 321, 65 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 521, 362, 321, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 521, 362, 321, 65 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 521, 362, 321, 65 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 521, 362, 321, 65 is 1.
HCF(521, 362, 321, 65) = 1
HCF of 521, 362, 321, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 521, 362, 321, 65 is 1.
Highest Common Factor of 521,362,321,65 is 1
Step 1: Since 521 > 362, we apply the division lemma to 521 and 362, to get
521 = 362 x 1 + 159
Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 159 and 362, to get
362 = 159 x 2 + 44
Step 3: We consider the new divisor 159 and the new remainder 44, and apply the division lemma to get
159 = 44 x 3 + 27
We consider the new divisor 44 and the new remainder 27,and apply the division lemma to get
44 = 27 x 1 + 17
We consider the new divisor 27 and the new remainder 17,and apply the division lemma to get
27 = 17 x 1 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 521 and 362 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(44,27) = HCF(159,44) = HCF(362,159) = HCF(521,362) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 321 > 1, we apply the division lemma to 321 and 1, to get
321 = 1 x 321 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 321 is 1
Notice that 1 = HCF(321,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 1, we apply the division lemma to 65 and 1, to get
65 = 1 x 65 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65 is 1
Notice that 1 = HCF(65,1) .
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Frequently Asked Questions on HCF of 521, 362, 321, 65 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 521, 362, 321, 65?
Answer: HCF of 521, 362, 321, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 521, 362, 321, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 521, 362, 321, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.