Highest Common Factor of 489, 4221 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, 4221 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 4221 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, 4221 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, 4221 is 3.
HCF(489, 4221) = 3
HCF of 489, 4221 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, 4221 is 3.
Highest Common Factor of 489,4221 is 3
Step 1: Since 4221 > 489, we apply the division lemma to 4221 and 489, to get
4221 = 489 x 8 + 309
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 309 and 489, to get
489 = 309 x 1 + 180
Step 3: We consider the new divisor 309 and the new remainder 180, and apply the division lemma to get
309 = 180 x 1 + 129
We consider the new divisor 180 and the new remainder 129,and apply the division lemma to get
180 = 129 x 1 + 51
We consider the new divisor 129 and the new remainder 51,and apply the division lemma to get
129 = 51 x 2 + 27
We consider the new divisor 51 and the new remainder 27,and apply the division lemma to get
51 = 27 x 1 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 489 and 4221 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(51,27) = HCF(129,51) = HCF(180,129) = HCF(309,180) = HCF(489,309) = HCF(4221,489) .
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Frequently Asked Questions on HCF of 489, 4221 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, 4221?
Answer: HCF of 489, 4221 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 4221 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 4221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.