Highest Common Factor of 421, 581, 89 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 421, 581, 89 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 581, 89 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 421, 581, 89 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 421, 581, 89 is 1.
HCF(421, 581, 89) = 1
HCF of 421, 581, 89 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 421, 581, 89 is 1.
Highest Common Factor of 421,581,89 is 1
Step 1: Since 581 > 421, we apply the division lemma to 581 and 421, to get
581 = 421 x 1 + 160
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 160 and 421, to get
421 = 160 x 2 + 101
Step 3: We consider the new divisor 160 and the new remainder 101, and apply the division lemma to get
160 = 101 x 1 + 59
We consider the new divisor 101 and the new remainder 59,and apply the division lemma to get
101 = 59 x 1 + 42
We consider the new divisor 59 and the new remainder 42,and apply the division lemma to get
59 = 42 x 1 + 17
We consider the new divisor 42 and the new remainder 17,and apply the division lemma to get
42 = 17 x 2 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 581 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(42,17) = HCF(59,42) = HCF(101,59) = HCF(160,101) = HCF(421,160) = HCF(581,421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 89 > 1, we apply the division lemma to 89 and 1, to get
89 = 1 x 89 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 89 is 1
Notice that 1 = HCF(89,1) .
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Frequently Asked Questions on HCF of 421, 581, 89 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 421, 581, 89?
Answer: HCF of 421, 581, 89 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 581, 89 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 581, 89 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.