Highest Common Factor of 486, 864, 234 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 486, 864, 234 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 486, 864, 234 is 18 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 486, 864, 234 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 486, 864, 234 is 18.
HCF(486, 864, 234) = 18
HCF of 486, 864, 234 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 486, 864, 234 is 18.
Highest Common Factor of 486,864,234 is 18
Step 1: Since 864 > 486, we apply the division lemma to 864 and 486, to get
864 = 486 x 1 + 378
Step 2: Since the reminder 486 ≠ 0, we apply division lemma to 378 and 486, to get
486 = 378 x 1 + 108
Step 3: We consider the new divisor 378 and the new remainder 108, and apply the division lemma to get
378 = 108 x 3 + 54
We consider the new divisor 108 and the new remainder 54, and apply the division lemma to get
108 = 54 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 486 and 864 is 54
Notice that 54 = HCF(108,54) = HCF(378,108) = HCF(486,378) = HCF(864,486) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 234 > 54, we apply the division lemma to 234 and 54, to get
234 = 54 x 4 + 18
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 18 and 54, to get
54 = 18 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 54 and 234 is 18
Notice that 18 = HCF(54,18) = HCF(234,54) .
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Frequently Asked Questions on HCF of 486, 864, 234 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 486, 864, 234?
Answer: HCF of 486, 864, 234 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 486, 864, 234 using Euclid's Algorithm?
Answer: For arbitrary numbers 486, 864, 234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.