Highest Common Factor of 1478, 3349, 31617 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 1478, 3349, 31617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1478, 3349, 31617 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 1478, 3349, 31617 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 1478, 3349, 31617 is 1.
HCF(1478, 3349, 31617) = 1
HCF of 1478, 3349, 31617 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1478, 3349, 31617 is 1.
Highest Common Factor of 1478,3349,31617 is 1
Step 1: Since 3349 > 1478, we apply the division lemma to 3349 and 1478, to get
3349 = 1478 x 2 + 393
Step 2: Since the reminder 1478 ≠ 0, we apply division lemma to 393 and 1478, to get
1478 = 393 x 3 + 299
Step 3: We consider the new divisor 393 and the new remainder 299, and apply the division lemma to get
393 = 299 x 1 + 94
We consider the new divisor 299 and the new remainder 94,and apply the division lemma to get
299 = 94 x 3 + 17
We consider the new divisor 94 and the new remainder 17,and apply the division lemma to get
94 = 17 x 5 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1478 and 3349 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(94,17) = HCF(299,94) = HCF(393,299) = HCF(1478,393) = HCF(3349,1478) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31617 > 1, we apply the division lemma to 31617 and 1, to get
31617 = 1 x 31617 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31617 is 1
Notice that 1 = HCF(31617,1) .
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Frequently Asked Questions on HCF of 1478, 3349, 31617 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 1478, 3349, 31617?
Answer: HCF of 1478, 3349, 31617 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1478, 3349, 31617 using Euclid's Algorithm?
Answer: For arbitrary numbers 1478, 3349, 31617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.