Highest Common Factor of 408, 987, 32 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 408, 987, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 987, 32 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 408, 987, 32 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 408, 987, 32 is 1.
HCF(408, 987, 32) = 1
HCF of 408, 987, 32 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 987, 32 is 1.
Highest Common Factor of 408,987,32 is 1
Step 1: Since 987 > 408, we apply the division lemma to 987 and 408, to get
987 = 408 x 2 + 171
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 171 and 408, to get
408 = 171 x 2 + 66
Step 3: We consider the new divisor 171 and the new remainder 66, and apply the division lemma to get
171 = 66 x 2 + 39
We consider the new divisor 66 and the new remainder 39,and apply the division lemma to get
66 = 39 x 1 + 27
We consider the new divisor 39 and the new remainder 27,and apply the division lemma to get
39 = 27 x 1 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 408 and 987 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(66,39) = HCF(171,66) = HCF(408,171) = HCF(987,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 3, we apply the division lemma to 32 and 3, to get
32 = 3 x 10 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 32 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) .
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Frequently Asked Questions on HCF of 408, 987, 32 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 408, 987, 32?
Answer: HCF of 408, 987, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 987, 32 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 987, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.