Highest Common Factor of 409, 987, 727 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 409, 987, 727 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 409, 987, 727 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 409, 987, 727 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 409, 987, 727 is 1.
HCF(409, 987, 727) = 1
HCF of 409, 987, 727 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 409, 987, 727 is 1.
Highest Common Factor of 409,987,727 is 1
Step 1: Since 987 > 409, we apply the division lemma to 987 and 409, to get
987 = 409 x 2 + 169
Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 169 and 409, to get
409 = 169 x 2 + 71
Step 3: We consider the new divisor 169 and the new remainder 71, and apply the division lemma to get
169 = 71 x 2 + 27
We consider the new divisor 71 and the new remainder 27,and apply the division lemma to get
71 = 27 x 2 + 17
We consider the new divisor 27 and the new remainder 17,and apply the division lemma to get
27 = 17 x 1 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 409 and 987 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(71,27) = HCF(169,71) = HCF(409,169) = HCF(987,409) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 727 > 1, we apply the division lemma to 727 and 1, to get
727 = 1 x 727 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 727 is 1
Notice that 1 = HCF(727,1) .
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Frequently Asked Questions on HCF of 409, 987, 727 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 409, 987, 727?
Answer: HCF of 409, 987, 727 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 409, 987, 727 using Euclid's Algorithm?
Answer: For arbitrary numbers 409, 987, 727 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.