Highest Common Factor of 414, 9709 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 414, 9709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 9709 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 414, 9709 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 414, 9709 is 1.
HCF(414, 9709) = 1
HCF of 414, 9709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 9709 is 1.
Highest Common Factor of 414,9709 is 1
Step 1: Since 9709 > 414, we apply the division lemma to 9709 and 414, to get
9709 = 414 x 23 + 187
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 187 and 414, to get
414 = 187 x 2 + 40
Step 3: We consider the new divisor 187 and the new remainder 40, and apply the division lemma to get
187 = 40 x 4 + 27
We consider the new divisor 40 and the new remainder 27,and apply the division lemma to get
40 = 27 x 1 + 13
We consider the new divisor 27 and the new remainder 13,and apply the division lemma to get
27 = 13 x 2 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 414 and 9709 is 1
Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(40,27) = HCF(187,40) = HCF(414,187) = HCF(9709,414) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 414, 9709 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 414, 9709?
Answer: HCF of 414, 9709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 9709 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 9709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
