Highest Common Factor of 408, 3172, 7147 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 408, 3172, 7147 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 3172, 7147 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 408, 3172, 7147 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 408, 3172, 7147 is 1.
HCF(408, 3172, 7147) = 1
HCF of 408, 3172, 7147 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 3172, 7147 is 1.
Highest Common Factor of 408,3172,7147 is 1
Step 1: Since 3172 > 408, we apply the division lemma to 3172 and 408, to get
3172 = 408 x 7 + 316
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 316 and 408, to get
408 = 316 x 1 + 92
Step 3: We consider the new divisor 316 and the new remainder 92, and apply the division lemma to get
316 = 92 x 3 + 40
We consider the new divisor 92 and the new remainder 40,and apply the division lemma to get
92 = 40 x 2 + 12
We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get
40 = 12 x 3 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 408 and 3172 is 4
Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(92,40) = HCF(316,92) = HCF(408,316) = HCF(3172,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7147 > 4, we apply the division lemma to 7147 and 4, to get
7147 = 4 x 1786 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 7147 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7147,4) .
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Frequently Asked Questions on HCF of 408, 3172, 7147 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 408, 3172, 7147?
Answer: HCF of 408, 3172, 7147 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 3172, 7147 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 3172, 7147 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.