Highest Common Factor of 997, 420 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 997, 420 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 420 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 997, 420 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 997, 420 is 1.
HCF(997, 420) = 1
HCF of 997, 420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 997, 420 is 1.
Highest Common Factor of 997,420 is 1
Step 1: Since 997 > 420, we apply the division lemma to 997 and 420, to get
997 = 420 x 2 + 157
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 157 and 420, to get
420 = 157 x 2 + 106
Step 3: We consider the new divisor 157 and the new remainder 106, and apply the division lemma to get
157 = 106 x 1 + 51
We consider the new divisor 106 and the new remainder 51,and apply the division lemma to get
106 = 51 x 2 + 4
We consider the new divisor 51 and the new remainder 4,and apply the division lemma to get
51 = 4 x 12 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 997 and 420 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(51,4) = HCF(106,51) = HCF(157,106) = HCF(420,157) = HCF(997,420) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 997, 420 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 997, 420?
Answer: HCF of 997, 420 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
