Highest Common Factor of 409, 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 409, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 409, 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 409, 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 409, 709 is 1.
HCF(409, 709) = 1
HCF of 409, 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 409, 709 is 1.
Highest Common Factor of 409,709 is 1
Step 1: Since 709 > 409, we apply the division lemma to 709 and 409, to get
709 = 409 x 1 + 300
Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 300 and 409, to get
409 = 300 x 1 + 109
Step 3: We consider the new divisor 300 and the new remainder 109, and apply the division lemma to get
300 = 109 x 2 + 82
We consider the new divisor 109 and the new remainder 82,and apply the division lemma to get
109 = 82 x 1 + 27
We consider the new divisor 82 and the new remainder 27,and apply the division lemma to get
82 = 27 x 3 + 1
We consider the new divisor 27 and the new remainder 1,and apply the division lemma to get
27 = 1 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 709 is 1
Notice that 1 = HCF(27,1) = HCF(82,27) = HCF(109,82) = HCF(300,109) = HCF(409,300) = HCF(709,409) .
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Frequently Asked Questions on HCF of 409, 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 409, 709?
Answer: HCF of 409, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 409, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 409, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.