Highest Common Factor of 420, 217 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 420, 217 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 217 is 7 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 420, 217 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 420, 217 is 7.
HCF(420, 217) = 7
HCF of 420, 217 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 217 is 7.
Highest Common Factor of 420,217 is 7
Step 1: Since 420 > 217, we apply the division lemma to 420 and 217, to get
420 = 217 x 1 + 203
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 203 and 217, to get
217 = 203 x 1 + 14
Step 3: We consider the new divisor 203 and the new remainder 14, and apply the division lemma to get
203 = 14 x 14 + 7
We consider the new divisor 14 and the new remainder 7, and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 420 and 217 is 7
Notice that 7 = HCF(14,7) = HCF(203,14) = HCF(217,203) = HCF(420,217) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 420, 217 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 420, 217?
Answer: HCF of 420, 217 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 217 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.