Highest Common Factor of 449, 709 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, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 449, 709 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, 709 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, 709 is 1.
HCF(449, 709) = 1
HCF of 449, 709 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, 709 is 1.
Highest Common Factor of 449,709 is 1
Step 1: Since 709 > 449, we apply the division lemma to 709 and 449, to get
709 = 449 x 1 + 260
Step 2: Since the reminder 449 ≠ 0, we apply division lemma to 260 and 449, to get
449 = 260 x 1 + 189
Step 3: We consider the new divisor 260 and the new remainder 189, and apply the division lemma to get
260 = 189 x 1 + 71
We consider the new divisor 189 and the new remainder 71,and apply the division lemma to get
189 = 71 x 2 + 47
We consider the new divisor 71 and the new remainder 47,and apply the division lemma to get
71 = 47 x 1 + 24
We consider the new divisor 47 and the new remainder 24,and apply the division lemma to get
47 = 24 x 1 + 23
We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get
24 = 23 x 1 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 449 and 709 is 1
Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(47,24) = HCF(71,47) = HCF(189,71) = HCF(260,189) = HCF(449,260) = HCF(709,449) .
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Frequently Asked Questions on HCF of 449, 709 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, 709?
Answer: HCF of 449, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 449, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 449, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.