Highest Common Factor of 729, 450, 366 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 729, 450, 366 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 450, 366 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 729, 450, 366 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 729, 450, 366 is 3.
HCF(729, 450, 366) = 3
HCF of 729, 450, 366 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 729, 450, 366 is 3.
Highest Common Factor of 729,450,366 is 3
Step 1: Since 729 > 450, we apply the division lemma to 729 and 450, to get
729 = 450 x 1 + 279
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 279 and 450, to get
450 = 279 x 1 + 171
Step 3: We consider the new divisor 279 and the new remainder 171, and apply the division lemma to get
279 = 171 x 1 + 108
We consider the new divisor 171 and the new remainder 108,and apply the division lemma to get
171 = 108 x 1 + 63
We consider the new divisor 108 and the new remainder 63,and apply the division lemma to get
108 = 63 x 1 + 45
We consider the new divisor 63 and the new remainder 45,and apply the division lemma to get
63 = 45 x 1 + 18
We consider the new divisor 45 and the new remainder 18,and apply the division lemma to get
45 = 18 x 2 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 729 and 450 is 9
Notice that 9 = HCF(18,9) = HCF(45,18) = HCF(63,45) = HCF(108,63) = HCF(171,108) = HCF(279,171) = HCF(450,279) = HCF(729,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 366 > 9, we apply the division lemma to 366 and 9, to get
366 = 9 x 40 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 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 9 and 366 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(366,9) .
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Frequently Asked Questions on HCF of 729, 450, 366 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 729, 450, 366?
Answer: HCF of 729, 450, 366 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 450, 366 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 450, 366 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.