Highest Common Factor of 747, 5838, 2189 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 747, 5838, 2189 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 747, 5838, 2189 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 747, 5838, 2189 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 747, 5838, 2189 is 1.
HCF(747, 5838, 2189) = 1
HCF of 747, 5838, 2189 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 747, 5838, 2189 is 1.
Highest Common Factor of 747,5838,2189 is 1
Step 1: Since 5838 > 747, we apply the division lemma to 5838 and 747, to get
5838 = 747 x 7 + 609
Step 2: Since the reminder 747 ≠ 0, we apply division lemma to 609 and 747, to get
747 = 609 x 1 + 138
Step 3: We consider the new divisor 609 and the new remainder 138, and apply the division lemma to get
609 = 138 x 4 + 57
We consider the new divisor 138 and the new remainder 57,and apply the division lemma to get
138 = 57 x 2 + 24
We consider the new divisor 57 and the new remainder 24,and apply the division lemma to get
57 = 24 x 2 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 747 and 5838 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(138,57) = HCF(609,138) = HCF(747,609) = HCF(5838,747) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2189 > 3, we apply the division lemma to 2189 and 3, to get
2189 = 3 x 729 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 2189 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(2189,3) .
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Frequently Asked Questions on HCF of 747, 5838, 2189 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 747, 5838, 2189?
Answer: HCF of 747, 5838, 2189 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 747, 5838, 2189 using Euclid's Algorithm?
Answer: For arbitrary numbers 747, 5838, 2189 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
