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 417, 575, 356 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 575, 356 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 417, 575, 356 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 417, 575, 356 is 1.
HCF(417, 575, 356) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 417, 575, 356 is 1.
Step 1: Since 575 > 417, we apply the division lemma to 575 and 417, to get
575 = 417 x 1 + 158
Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 158 and 417, to get
417 = 158 x 2 + 101
Step 3: We consider the new divisor 158 and the new remainder 101, and apply the division lemma to get
158 = 101 x 1 + 57
We consider the new divisor 101 and the new remainder 57,and apply the division lemma to get
101 = 57 x 1 + 44
We consider the new divisor 57 and the new remainder 44,and apply the division lemma to get
57 = 44 x 1 + 13
We consider the new divisor 44 and the new remainder 13,and apply the division lemma to get
44 = 13 x 3 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 417 and 575 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(44,13) = HCF(57,44) = HCF(101,57) = HCF(158,101) = HCF(417,158) = HCF(575,417) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 356 > 1, we apply the division lemma to 356 and 1, to get
356 = 1 x 356 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 356 is 1
Notice that 1 = HCF(356,1) .
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 417, 575, 356?
Answer: HCF of 417, 575, 356 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 575, 356 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 575, 356 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.