Highest Common Factor of 8172, 1785, 55743 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 8172, 1785, 55743 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8172, 1785, 55743 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 8172, 1785, 55743 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 8172, 1785, 55743 is 3.
HCF(8172, 1785, 55743) = 3
HCF of 8172, 1785, 55743 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8172, 1785, 55743 is 3.
Highest Common Factor of 8172,1785,55743 is 3
Step 1: Since 8172 > 1785, we apply the division lemma to 8172 and 1785, to get
8172 = 1785 x 4 + 1032
Step 2: Since the reminder 1785 ≠ 0, we apply division lemma to 1032 and 1785, to get
1785 = 1032 x 1 + 753
Step 3: We consider the new divisor 1032 and the new remainder 753, and apply the division lemma to get
1032 = 753 x 1 + 279
We consider the new divisor 753 and the new remainder 279,and apply the division lemma to get
753 = 279 x 2 + 195
We consider the new divisor 279 and the new remainder 195,and apply the division lemma to get
279 = 195 x 1 + 84
We consider the new divisor 195 and the new remainder 84,and apply the division lemma to get
195 = 84 x 2 + 27
We consider the new divisor 84 and the new remainder 27,and apply the division lemma to get
84 = 27 x 3 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8172 and 1785 is 3
Notice that 3 = HCF(27,3) = HCF(84,27) = HCF(195,84) = HCF(279,195) = HCF(753,279) = HCF(1032,753) = HCF(1785,1032) = HCF(8172,1785) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55743 > 3, we apply the division lemma to 55743 and 3, to get
55743 = 3 x 18581 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 55743 is 3
Notice that 3 = HCF(55743,3) .
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Frequently Asked Questions on HCF of 8172, 1785, 55743 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 8172, 1785, 55743?
Answer: HCF of 8172, 1785, 55743 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8172, 1785, 55743 using Euclid's Algorithm?
Answer: For arbitrary numbers 8172, 1785, 55743 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.