Highest Common Factor of 489, 8574, 3000 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, 8574, 3000 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 8574, 3000 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, 8574, 3000 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, 8574, 3000 is 3.
HCF(489, 8574, 3000) = 3
HCF of 489, 8574, 3000 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, 8574, 3000 is 3.
Highest Common Factor of 489,8574,3000 is 3
Step 1: Since 8574 > 489, we apply the division lemma to 8574 and 489, to get
8574 = 489 x 17 + 261
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 261 and 489, to get
489 = 261 x 1 + 228
Step 3: We consider the new divisor 261 and the new remainder 228, and apply the division lemma to get
261 = 228 x 1 + 33
We consider the new divisor 228 and the new remainder 33,and apply the division lemma to get
228 = 33 x 6 + 30
We consider the new divisor 33 and the new remainder 30,and apply the division lemma to get
33 = 30 x 1 + 3
We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get
30 = 3 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 489 and 8574 is 3
Notice that 3 = HCF(30,3) = HCF(33,30) = HCF(228,33) = HCF(261,228) = HCF(489,261) = HCF(8574,489) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3000 > 3, we apply the division lemma to 3000 and 3, to get
3000 = 3 x 1000 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 3000 is 3
Notice that 3 = HCF(3000,3) .
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Frequently Asked Questions on HCF of 489, 8574, 3000 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, 8574, 3000?
Answer: HCF of 489, 8574, 3000 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 8574, 3000 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 8574, 3000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.