Highest Common Factor of 397, 728, 12 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 397, 728, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 397, 728, 12 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 397, 728, 12 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 397, 728, 12 is 1.
HCF(397, 728, 12) = 1
HCF of 397, 728, 12 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 397, 728, 12 is 1.
Highest Common Factor of 397,728,12 is 1
Step 1: Since 728 > 397, we apply the division lemma to 728 and 397, to get
728 = 397 x 1 + 331
Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 331 and 397, to get
397 = 331 x 1 + 66
Step 3: We consider the new divisor 331 and the new remainder 66, and apply the division lemma to get
331 = 66 x 5 + 1
We consider the new divisor 66 and the new remainder 1, and apply the division lemma to get
66 = 1 x 66 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 397 and 728 is 1
Notice that 1 = HCF(66,1) = HCF(331,66) = HCF(397,331) = HCF(728,397) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1
Notice that 1 = HCF(12,1) .
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Frequently Asked Questions on HCF of 397, 728, 12 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 397, 728, 12?
Answer: HCF of 397, 728, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 397, 728, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 397, 728, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.