Highest Common Factor of 423, 160 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 423, 160 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 160 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 423, 160 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 423, 160 is 1.
HCF(423, 160) = 1
HCF of 423, 160 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 423, 160 is 1.
Highest Common Factor of 423,160 is 1
Step 1: Since 423 > 160, we apply the division lemma to 423 and 160, to get
423 = 160 x 2 + 103
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 103 and 160, to get
160 = 103 x 1 + 57
Step 3: We consider the new divisor 103 and the new remainder 57, and apply the division lemma to get
103 = 57 x 1 + 46
We consider the new divisor 57 and the new remainder 46,and apply the division lemma to get
57 = 46 x 1 + 11
We consider the new divisor 46 and the new remainder 11,and apply the division lemma to get
46 = 11 x 4 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 423 and 160 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(46,11) = HCF(57,46) = HCF(103,57) = HCF(160,103) = HCF(423,160) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 423, 160 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 423, 160?
Answer: HCF of 423, 160 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 160 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.