Highest Common Factor of 554, 1445, 1728 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 554, 1445, 1728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 554, 1445, 1728 is 1 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 554, 1445, 1728 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 554, 1445, 1728 is 1.
HCF(554, 1445, 1728) = 1
HCF of 554, 1445, 1728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 554, 1445, 1728 is 1.
Highest Common Factor of 554,1445,1728 is 1
Step 1: Since 1445 > 554, we apply the division lemma to 1445 and 554, to get
1445 = 554 x 2 + 337
Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 337 and 554, to get
554 = 337 x 1 + 217
Step 3: We consider the new divisor 337 and the new remainder 217, and apply the division lemma to get
337 = 217 x 1 + 120
We consider the new divisor 217 and the new remainder 120,and apply the division lemma to get
217 = 120 x 1 + 97
We consider the new divisor 120 and the new remainder 97,and apply the division lemma to get
120 = 97 x 1 + 23
We consider the new divisor 97 and the new remainder 23,and apply the division lemma to get
97 = 23 x 4 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 554 and 1445 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(97,23) = HCF(120,97) = HCF(217,120) = HCF(337,217) = HCF(554,337) = HCF(1445,554) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1728 > 1, we apply the division lemma to 1728 and 1, to get
1728 = 1 x 1728 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1728 is 1
Notice that 1 = HCF(1728,1) .
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Frequently Asked Questions on HCF of 554, 1445, 1728 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 554, 1445, 1728?
Answer: HCF of 554, 1445, 1728 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 554, 1445, 1728 using Euclid's Algorithm?
Answer: For arbitrary numbers 554, 1445, 1728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
