Highest Common Factor of 489, 27731 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, 27731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 27731 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, 27731 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, 27731 is 1.
HCF(489, 27731) = 1
HCF of 489, 27731 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, 27731 is 1.
Highest Common Factor of 489,27731 is 1
Step 1: Since 27731 > 489, we apply the division lemma to 27731 and 489, to get
27731 = 489 x 56 + 347
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 347 and 489, to get
489 = 347 x 1 + 142
Step 3: We consider the new divisor 347 and the new remainder 142, and apply the division lemma to get
347 = 142 x 2 + 63
We consider the new divisor 142 and the new remainder 63,and apply the division lemma to get
142 = 63 x 2 + 16
We consider the new divisor 63 and the new remainder 16,and apply the division lemma to get
63 = 16 x 3 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 489 and 27731 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(63,16) = HCF(142,63) = HCF(347,142) = HCF(489,347) = HCF(27731,489) .
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Frequently Asked Questions on HCF of 489, 27731 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, 27731?
Answer: HCF of 489, 27731 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 27731 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 27731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.