Highest Common Factor of 489, 45172 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 489, 45172 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 45172 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 489, 45172 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 489, 45172 is 1.
HCF(489, 45172) = 1
HCF of 489, 45172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 489, 45172 is 1.
Highest Common Factor of 489,45172 is 1
Step 1: Since 45172 > 489, we apply the division lemma to 45172 and 489, to get
45172 = 489 x 92 + 184
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 184 and 489, to get
489 = 184 x 2 + 121
Step 3: We consider the new divisor 184 and the new remainder 121, and apply the division lemma to get
184 = 121 x 1 + 63
We consider the new divisor 121 and the new remainder 63,and apply the division lemma to get
121 = 63 x 1 + 58
We consider the new divisor 63 and the new remainder 58,and apply the division lemma to get
63 = 58 x 1 + 5
We consider the new divisor 58 and the new remainder 5,and apply the division lemma to get
58 = 5 x 11 + 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 489 and 45172 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(58,5) = HCF(63,58) = HCF(121,63) = HCF(184,121) = HCF(489,184) = HCF(45172,489) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 489, 45172 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 489, 45172?
Answer: HCF of 489, 45172 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 45172 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 45172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
