Highest Common Factor of 449, 997, 674 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 449, 997, 674 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 449, 997, 674 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 449, 997, 674 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 449, 997, 674 is 1.
HCF(449, 997, 674) = 1
HCF of 449, 997, 674 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 449, 997, 674 is 1.
Highest Common Factor of 449,997,674 is 1
Step 1: Since 997 > 449, we apply the division lemma to 997 and 449, to get
997 = 449 x 2 + 99
Step 2: Since the reminder 449 ≠ 0, we apply division lemma to 99 and 449, to get
449 = 99 x 4 + 53
Step 3: We consider the new divisor 99 and the new remainder 53, and apply the division lemma to get
99 = 53 x 1 + 46
We consider the new divisor 53 and the new remainder 46,and apply the division lemma to get
53 = 46 x 1 + 7
We consider the new divisor 46 and the new remainder 7,and apply the division lemma to get
46 = 7 x 6 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
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 449 and 997 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(46,7) = HCF(53,46) = HCF(99,53) = HCF(449,99) = HCF(997,449) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 674 > 1, we apply the division lemma to 674 and 1, to get
674 = 1 x 674 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 674 is 1
Notice that 1 = HCF(674,1) .
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Frequently Asked Questions on HCF of 449, 997, 674 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 449, 997, 674?
Answer: HCF of 449, 997, 674 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 449, 997, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 449, 997, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.