Highest Common Factor of 532, 921, 408 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 532, 921, 408 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 532, 921, 408 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, 921, 408 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, 921, 408 is 1.
HCF(532, 921, 408) = 1
HCF of 532, 921, 408 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 532, 921, 408 is 1.
Highest Common Factor of 532,921,408 is 1
Step 1: Since 921 > 532, we apply the division lemma to 921 and 532, to get
921 = 532 x 1 + 389
Step 2: Since the reminder 532 ≠ 0, we apply division lemma to 389 and 532, to get
532 = 389 x 1 + 143
Step 3: We consider the new divisor 389 and the new remainder 143, and apply the division lemma to get
389 = 143 x 2 + 103
We consider the new divisor 143 and the new remainder 103,and apply the division lemma to get
143 = 103 x 1 + 40
We consider the new divisor 103 and the new remainder 40,and apply the division lemma to get
103 = 40 x 2 + 23
We consider the new divisor 40 and the new remainder 23,and apply the division lemma to get
40 = 23 x 1 + 17
We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get
23 = 17 x 1 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 532 and 921 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(40,23) = HCF(103,40) = HCF(143,103) = HCF(389,143) = HCF(532,389) = HCF(921,532) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 408 > 1, we apply the division lemma to 408 and 1, to get
408 = 1 x 408 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 408 is 1
Notice that 1 = HCF(408,1) .
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Frequently Asked Questions on HCF of 532, 921, 408 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 532, 921, 408?
Answer: HCF of 532, 921, 408 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 532, 921, 408 using Euclid's Algorithm?
Answer: For arbitrary numbers 532, 921, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.