Highest Common Factor of 1854, 8349, 81149 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 1854, 8349, 81149 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1854, 8349, 81149 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 1854, 8349, 81149 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 1854, 8349, 81149 is 1.
HCF(1854, 8349, 81149) = 1
HCF of 1854, 8349, 81149 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1854, 8349, 81149 is 1.
Highest Common Factor of 1854,8349,81149 is 1
Step 1: Since 8349 > 1854, we apply the division lemma to 8349 and 1854, to get
8349 = 1854 x 4 + 933
Step 2: Since the reminder 1854 ≠ 0, we apply division lemma to 933 and 1854, to get
1854 = 933 x 1 + 921
Step 3: We consider the new divisor 933 and the new remainder 921, and apply the division lemma to get
933 = 921 x 1 + 12
We consider the new divisor 921 and the new remainder 12,and apply the division lemma to get
921 = 12 x 76 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1854 and 8349 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(921,12) = HCF(933,921) = HCF(1854,933) = HCF(8349,1854) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81149 > 3, we apply the division lemma to 81149 and 3, to get
81149 = 3 x 27049 + 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 81149 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(81149,3) .
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Frequently Asked Questions on HCF of 1854, 8349, 81149 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 1854, 8349, 81149?
Answer: HCF of 1854, 8349, 81149 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1854, 8349, 81149 using Euclid's Algorithm?
Answer: For arbitrary numbers 1854, 8349, 81149 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
