Highest Common Factor of 417, 570 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 417, 570 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 570 is 3 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, 570 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, 570 is 3.
HCF(417, 570) = 3
HCF of 417, 570 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 417, 570 is 3.
Highest Common Factor of 417,570 is 3
Step 1: Since 570 > 417, we apply the division lemma to 570 and 417, to get
570 = 417 x 1 + 153
Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 153 and 417, to get
417 = 153 x 2 + 111
Step 3: We consider the new divisor 153 and the new remainder 111, and apply the division lemma to get
153 = 111 x 1 + 42
We consider the new divisor 111 and the new remainder 42,and apply the division lemma to get
111 = 42 x 2 + 27
We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get
42 = 27 x 1 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 417 and 570 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(111,42) = HCF(153,111) = HCF(417,153) = HCF(570,417) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 417, 570 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 417, 570?
Answer: HCF of 417, 570 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 570 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 570 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.