Highest Common Factor of 489, 58992 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, 58992 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 58992 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 489, 58992 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, 58992 is 3.
HCF(489, 58992) = 3
HCF of 489, 58992 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, 58992 is 3.
Highest Common Factor of 489,58992 is 3
Step 1: Since 58992 > 489, we apply the division lemma to 58992 and 489, to get
58992 = 489 x 120 + 312
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 312 and 489, to get
489 = 312 x 1 + 177
Step 3: We consider the new divisor 312 and the new remainder 177, and apply the division lemma to get
312 = 177 x 1 + 135
We consider the new divisor 177 and the new remainder 135,and apply the division lemma to get
177 = 135 x 1 + 42
We consider the new divisor 135 and the new remainder 42,and apply the division lemma to get
135 = 42 x 3 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 489 and 58992 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(135,42) = HCF(177,135) = HCF(312,177) = HCF(489,312) = HCF(58992,489) .
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Frequently Asked Questions on HCF of 489, 58992 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, 58992?
Answer: HCF of 489, 58992 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 58992 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 58992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.