Highest Common Factor of 102, 462, 132, 729 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 102, 462, 132, 729 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 102, 462, 132, 729 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 102, 462, 132, 729 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 102, 462, 132, 729 is 3.
HCF(102, 462, 132, 729) = 3
HCF of 102, 462, 132, 729 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 102, 462, 132, 729 is 3.
Highest Common Factor of 102,462,132,729 is 3
Step 1: Since 462 > 102, we apply the division lemma to 462 and 102, to get
462 = 102 x 4 + 54
Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 54 and 102, to get
102 = 54 x 1 + 48
Step 3: We consider the new divisor 54 and the new remainder 48, and apply the division lemma to get
54 = 48 x 1 + 6
We consider the new divisor 48 and the new remainder 6, and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 102 and 462 is 6
Notice that 6 = HCF(48,6) = HCF(54,48) = HCF(102,54) = HCF(462,102) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 132 > 6, we apply the division lemma to 132 and 6, to get
132 = 6 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 132 is 6
Notice that 6 = HCF(132,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 729 > 6, we apply the division lemma to 729 and 6, to get
729 = 6 x 121 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 729 is 3
Notice that 3 = HCF(6,3) = HCF(729,6) .
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Frequently Asked Questions on HCF of 102, 462, 132, 729 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 102, 462, 132, 729?
Answer: HCF of 102, 462, 132, 729 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 102, 462, 132, 729 using Euclid's Algorithm?
Answer: For arbitrary numbers 102, 462, 132, 729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.