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, 572, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 572, 649 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, 572, 649 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, 572, 649 is 1.
HCF(412, 572, 649) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 572, 649 is 1.
Step 1: Since 572 > 412, we apply the division lemma to 572 and 412, to get
572 = 412 x 1 + 160
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 160 and 412, to get
412 = 160 x 2 + 92
Step 3: We consider the new divisor 160 and the new remainder 92, and apply the division lemma to get
160 = 92 x 1 + 68
We consider the new divisor 92 and the new remainder 68,and apply the division lemma to get
92 = 68 x 1 + 24
We consider the new divisor 68 and the new remainder 24,and apply the division lemma to get
68 = 24 x 2 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 572 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(68,24) = HCF(92,68) = HCF(160,92) = HCF(412,160) = HCF(572,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 649 > 4, we apply the division lemma to 649 and 4, to get
649 = 4 x 162 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 649 is 1
Notice that 1 = HCF(4,1) = HCF(649,4) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 572, 649?
Answer: HCF of 412, 572, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 572, 649 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 572, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.