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 532, 218, 409 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 532, 218, 409 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 532, 218, 409 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 532, 218, 409 is 1.
HCF(532, 218, 409) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 532, 218, 409 is 1.
Step 1: Since 532 > 218, we apply the division lemma to 532 and 218, to get
532 = 218 x 2 + 96
Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 96 and 218, to get
218 = 96 x 2 + 26
Step 3: We consider the new divisor 96 and the new remainder 26, and apply the division lemma to get
96 = 26 x 3 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 532 and 218 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(96,26) = HCF(218,96) = HCF(532,218) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 409 > 2, we apply the division lemma to 409 and 2, to get
409 = 2 x 204 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 409 is 1
Notice that 1 = HCF(2,1) = HCF(409,2) .
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 532, 218, 409?
Answer: HCF of 532, 218, 409 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 532, 218, 409 using Euclid's Algorithm?
Answer: For arbitrary numbers 532, 218, 409 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.