Highest Common Factor of 412, 652, 394 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, 652, 394 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 652, 394 is 2 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, 652, 394 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, 652, 394 is 2.
HCF(412, 652, 394) = 2
HCF of 412, 652, 394 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, 652, 394 is 2.
Highest Common Factor of 412,652,394 is 2
Step 1: Since 652 > 412, we apply the division lemma to 652 and 412, to get
652 = 412 x 1 + 240
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 240 and 412, to get
412 = 240 x 1 + 172
Step 3: We consider the new divisor 240 and the new remainder 172, and apply the division lemma to get
240 = 172 x 1 + 68
We consider the new divisor 172 and the new remainder 68,and apply the division lemma to get
172 = 68 x 2 + 36
We consider the new divisor 68 and the new remainder 36,and apply the division lemma to get
68 = 36 x 1 + 32
We consider the new divisor 36 and the new remainder 32,and apply the division lemma to get
36 = 32 x 1 + 4
We consider the new divisor 32 and the new remainder 4,and apply the division lemma to get
32 = 4 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 652 is 4
Notice that 4 = HCF(32,4) = HCF(36,32) = HCF(68,36) = HCF(172,68) = HCF(240,172) = HCF(412,240) = HCF(652,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 394 > 4, we apply the division lemma to 394 and 4, to get
394 = 4 x 98 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 394 is 2
Notice that 2 = HCF(4,2) = HCF(394,4) .
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, 652, 394 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, 652, 394?
Answer: HCF of 412, 652, 394 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 652, 394 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 652, 394 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.