Highest Common Factor of 648, 873, 732 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, 873, 732 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 873, 732 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, 873, 732 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, 873, 732 is 3.
HCF(648, 873, 732) = 3
HCF of 648, 873, 732 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, 873, 732 is 3.
Highest Common Factor of 648,873,732 is 3
Step 1: Since 873 > 648, we apply the division lemma to 873 and 648, to get
873 = 648 x 1 + 225
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 225 and 648, to get
648 = 225 x 2 + 198
Step 3: We consider the new divisor 225 and the new remainder 198, and apply the division lemma to get
225 = 198 x 1 + 27
We consider the new divisor 198 and the new remainder 27,and apply the division lemma to get
198 = 27 x 7 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 648 and 873 is 9
Notice that 9 = HCF(27,9) = HCF(198,27) = HCF(225,198) = HCF(648,225) = HCF(873,648) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 732 > 9, we apply the division lemma to 732 and 9, to get
732 = 9 x 81 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 732 is 3
Notice that 3 = HCF(9,3) = HCF(732,9) .
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Frequently Asked Questions on HCF of 648, 873, 732 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, 873, 732?
Answer: HCF of 648, 873, 732 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 873, 732 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 873, 732 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.