Highest Common Factor of 588, 882, 216 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 588, 882, 216 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 882, 216 is 6 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 588, 882, 216 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 588, 882, 216 is 6.
HCF(588, 882, 216) = 6
HCF of 588, 882, 216 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 588, 882, 216 is 6.
Highest Common Factor of 588,882,216 is 6
Step 1: Since 882 > 588, we apply the division lemma to 882 and 588, to get
882 = 588 x 1 + 294
Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 294 and 588, to get
588 = 294 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 294, the HCF of 588 and 882 is 294
Notice that 294 = HCF(588,294) = HCF(882,588) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 294 > 216, we apply the division lemma to 294 and 216, to get
294 = 216 x 1 + 78
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 78 and 216, to get
216 = 78 x 2 + 60
Step 3: We consider the new divisor 78 and the new remainder 60, and apply the division lemma to get
78 = 60 x 1 + 18
We consider the new divisor 60 and the new remainder 18,and apply the division lemma to get
60 = 18 x 3 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 294 and 216 is 6
Notice that 6 = HCF(18,6) = HCF(60,18) = HCF(78,60) = HCF(216,78) = HCF(294,216) .
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Frequently Asked Questions on HCF of 588, 882, 216 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 588, 882, 216?
Answer: HCF of 588, 882, 216 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 882, 216 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 882, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.