Highest Common Factor of 7578, 5511, 54462 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 7578, 5511, 54462 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7578, 5511, 54462 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 7578, 5511, 54462 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 7578, 5511, 54462 is 3.
HCF(7578, 5511, 54462) = 3
HCF of 7578, 5511, 54462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7578, 5511, 54462 is 3.
Highest Common Factor of 7578,5511,54462 is 3
Step 1: Since 7578 > 5511, we apply the division lemma to 7578 and 5511, to get
7578 = 5511 x 1 + 2067
Step 2: Since the reminder 5511 ≠ 0, we apply division lemma to 2067 and 5511, to get
5511 = 2067 x 2 + 1377
Step 3: We consider the new divisor 2067 and the new remainder 1377, and apply the division lemma to get
2067 = 1377 x 1 + 690
We consider the new divisor 1377 and the new remainder 690,and apply the division lemma to get
1377 = 690 x 1 + 687
We consider the new divisor 690 and the new remainder 687,and apply the division lemma to get
690 = 687 x 1 + 3
We consider the new divisor 687 and the new remainder 3,and apply the division lemma to get
687 = 3 x 229 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7578 and 5511 is 3
Notice that 3 = HCF(687,3) = HCF(690,687) = HCF(1377,690) = HCF(2067,1377) = HCF(5511,2067) = HCF(7578,5511) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54462 > 3, we apply the division lemma to 54462 and 3, to get
54462 = 3 x 18154 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 54462 is 3
Notice that 3 = HCF(54462,3) .
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Frequently Asked Questions on HCF of 7578, 5511, 54462 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 7578, 5511, 54462?
Answer: HCF of 7578, 5511, 54462 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7578, 5511, 54462 using Euclid's Algorithm?
Answer: For arbitrary numbers 7578, 5511, 54462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.