Highest Common Factor of 8452, 8209 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 8452, 8209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8452, 8209 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 8452, 8209 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 8452, 8209 is 1.
HCF(8452, 8209) = 1
HCF of 8452, 8209 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8452, 8209 is 1.
Highest Common Factor of 8452,8209 is 1
Step 1: Since 8452 > 8209, we apply the division lemma to 8452 and 8209, to get
8452 = 8209 x 1 + 243
Step 2: Since the reminder 8209 ≠ 0, we apply division lemma to 243 and 8209, to get
8209 = 243 x 33 + 190
Step 3: We consider the new divisor 243 and the new remainder 190, and apply the division lemma to get
243 = 190 x 1 + 53
We consider the new divisor 190 and the new remainder 53,and apply the division lemma to get
190 = 53 x 3 + 31
We consider the new divisor 53 and the new remainder 31,and apply the division lemma to get
53 = 31 x 1 + 22
We consider the new divisor 31 and the new remainder 22,and apply the division lemma to get
31 = 22 x 1 + 9
We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get
22 = 9 x 2 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8452 and 8209 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(31,22) = HCF(53,31) = HCF(190,53) = HCF(243,190) = HCF(8209,243) = HCF(8452,8209) .
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Frequently Asked Questions on HCF of 8452, 8209 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 8452, 8209?
Answer: HCF of 8452, 8209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8452, 8209 using Euclid's Algorithm?
Answer: For arbitrary numbers 8452, 8209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
