Highest Common Factor of 3409, 7994, 43471 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 3409, 7994, 43471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3409, 7994, 43471 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 3409, 7994, 43471 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 3409, 7994, 43471 is 1.
HCF(3409, 7994, 43471) = 1
HCF of 3409, 7994, 43471 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3409, 7994, 43471 is 1.
Highest Common Factor of 3409,7994,43471 is 1
Step 1: Since 7994 > 3409, we apply the division lemma to 7994 and 3409, to get
7994 = 3409 x 2 + 1176
Step 2: Since the reminder 3409 ≠ 0, we apply division lemma to 1176 and 3409, to get
3409 = 1176 x 2 + 1057
Step 3: We consider the new divisor 1176 and the new remainder 1057, and apply the division lemma to get
1176 = 1057 x 1 + 119
We consider the new divisor 1057 and the new remainder 119,and apply the division lemma to get
1057 = 119 x 8 + 105
We consider the new divisor 119 and the new remainder 105,and apply the division lemma to get
119 = 105 x 1 + 14
We consider the new divisor 105 and the new remainder 14,and apply the division lemma to get
105 = 14 x 7 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 3409 and 7994 is 7
Notice that 7 = HCF(14,7) = HCF(105,14) = HCF(119,105) = HCF(1057,119) = HCF(1176,1057) = HCF(3409,1176) = HCF(7994,3409) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43471 > 7, we apply the division lemma to 43471 and 7, to get
43471 = 7 x 6210 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 43471 is 1
Notice that 1 = HCF(7,1) = HCF(43471,7) .
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Frequently Asked Questions on HCF of 3409, 7994, 43471 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 3409, 7994, 43471?
Answer: HCF of 3409, 7994, 43471 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3409, 7994, 43471 using Euclid's Algorithm?
Answer: For arbitrary numbers 3409, 7994, 43471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.