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, 405, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 405, 421 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, 405, 421 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, 405, 421 is 1.
HCF(558, 405, 421) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 405, 421 is 1.
Step 1: Since 558 > 405, we apply the division lemma to 558 and 405, to get
558 = 405 x 1 + 153
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 153 and 405, to get
405 = 153 x 2 + 99
Step 3: We consider the new divisor 153 and the new remainder 99, and apply the division lemma to get
153 = 99 x 1 + 54
We consider the new divisor 99 and the new remainder 54,and apply the division lemma to get
99 = 54 x 1 + 45
We consider the new divisor 54 and the new remainder 45,and apply the division lemma to get
54 = 45 x 1 + 9
We consider the new divisor 45 and the new remainder 9,and apply the division lemma to get
45 = 9 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 558 and 405 is 9
Notice that 9 = HCF(45,9) = HCF(54,45) = HCF(99,54) = HCF(153,99) = HCF(405,153) = HCF(558,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 9, we apply the division lemma to 421 and 9, to get
421 = 9 x 46 + 7
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 7 and 9, to get
9 = 7 x 1 + 2
Step 3: We consider the new divisor 7 and the new remainder 2, and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 421 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(421,9) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 405, 421?
Answer: HCF of 558, 405, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 405, 421 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 405, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.