Highest Common Factor of 558, 219, 397 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 558, 219, 397 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 219, 397 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 558, 219, 397 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 558, 219, 397 is 1.
HCF(558, 219, 397) = 1
HCF of 558, 219, 397 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 219, 397 is 1.
Highest Common Factor of 558,219,397 is 1
Step 1: Since 558 > 219, we apply the division lemma to 558 and 219, to get
558 = 219 x 2 + 120
Step 2: Since the reminder 219 ≠ 0, we apply division lemma to 120 and 219, to get
219 = 120 x 1 + 99
Step 3: We consider the new divisor 120 and the new remainder 99, and apply the division lemma to get
120 = 99 x 1 + 21
We consider the new divisor 99 and the new remainder 21,and apply the division lemma to get
99 = 21 x 4 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 558 and 219 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(99,21) = HCF(120,99) = HCF(219,120) = HCF(558,219) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 397 > 3, we apply the division lemma to 397 and 3, to get
397 = 3 x 132 + 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 397 is 1
Notice that 1 = HCF(3,1) = HCF(397,3) .
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Frequently Asked Questions on HCF of 558, 219, 397 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 558, 219, 397?
Answer: HCF of 558, 219, 397 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 219, 397 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 219, 397 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.