Highest Common Factor of 489, 76716 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, 76716 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 76716 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, 76716 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, 76716 is 3.
HCF(489, 76716) = 3
HCF of 489, 76716 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, 76716 is 3.
Highest Common Factor of 489,76716 is 3
Step 1: Since 76716 > 489, we apply the division lemma to 76716 and 489, to get
76716 = 489 x 156 + 432
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 432 and 489, to get
489 = 432 x 1 + 57
Step 3: We consider the new divisor 432 and the new remainder 57, and apply the division lemma to get
432 = 57 x 7 + 33
We consider the new divisor 57 and the new remainder 33,and apply the division lemma to get
57 = 33 x 1 + 24
We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 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 76716 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(57,33) = HCF(432,57) = HCF(489,432) = HCF(76716,489) .
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Frequently Asked Questions on HCF of 489, 76716 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, 76716?
Answer: HCF of 489, 76716 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 76716 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 76716 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.