Highest Common Factor of 648, 243, 744 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 648, 243, 744 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 243, 744 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 648, 243, 744 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 648, 243, 744 is 3.
HCF(648, 243, 744) = 3
HCF of 648, 243, 744 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 243, 744 is 3.
Highest Common Factor of 648,243,744 is 3
Step 1: Since 648 > 243, we apply the division lemma to 648 and 243, to get
648 = 243 x 2 + 162
Step 2: Since the reminder 243 ≠ 0, we apply division lemma to 162 and 243, to get
243 = 162 x 1 + 81
Step 3: We consider the new divisor 162 and the new remainder 81, and apply the division lemma to get
162 = 81 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 81, the HCF of 648 and 243 is 81
Notice that 81 = HCF(162,81) = HCF(243,162) = HCF(648,243) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 744 > 81, we apply the division lemma to 744 and 81, to get
744 = 81 x 9 + 15
Step 2: Since the reminder 81 ≠ 0, we apply division lemma to 15 and 81, to get
81 = 15 x 5 + 6
Step 3: We consider the new divisor 15 and the new remainder 6, and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma 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 81 and 744 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(81,15) = HCF(744,81) .
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Frequently Asked Questions on HCF of 648, 243, 744 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 648, 243, 744?
Answer: HCF of 648, 243, 744 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 243, 744 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 243, 744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.