Highest Common Factor of 412, 728, 147 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 412, 728, 147 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 728, 147 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 412, 728, 147 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 412, 728, 147 is 1.
HCF(412, 728, 147) = 1
HCF of 412, 728, 147 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 728, 147 is 1.
Highest Common Factor of 412,728,147 is 1
Step 1: Since 728 > 412, we apply the division lemma to 728 and 412, to get
728 = 412 x 1 + 316
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 316 and 412, to get
412 = 316 x 1 + 96
Step 3: We consider the new divisor 316 and the new remainder 96, and apply the division lemma to get
316 = 96 x 3 + 28
We consider the new divisor 96 and the new remainder 28,and apply the division lemma to get
96 = 28 x 3 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 728 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(96,28) = HCF(316,96) = HCF(412,316) = HCF(728,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 147 > 4, we apply the division lemma to 147 and 4, to get
147 = 4 x 36 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: 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 4 and 147 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(147,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 412, 728, 147 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 412, 728, 147?
Answer: HCF of 412, 728, 147 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 728, 147 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 728, 147 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.