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 406, 870, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 406, 870, 41 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 406, 870, 41 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 406, 870, 41 is 1.
HCF(406, 870, 41) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 406, 870, 41 is 1.
Step 1: Since 870 > 406, we apply the division lemma to 870 and 406, to get
870 = 406 x 2 + 58
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 58 and 406, to get
406 = 58 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 58, the HCF of 406 and 870 is 58
Notice that 58 = HCF(406,58) = HCF(870,406) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 58 > 41, we apply the division lemma to 58 and 41, to get
58 = 41 x 1 + 17
Step 2: Since the reminder 41 ≠ 0, we apply division lemma to 17 and 41, to get
41 = 17 x 2 + 7
Step 3: We consider the new divisor 17 and the new remainder 7, and apply the division lemma to get
17 = 7 x 2 + 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 58 and 41 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(41,17) = HCF(58,41) .
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 406, 870, 41?
Answer: HCF of 406, 870, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 406, 870, 41 using Euclid's Algorithm?
Answer: For arbitrary numbers 406, 870, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.