Highest Common Factor of 361, 209 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 361, 209 i.e. 19 the largest integer that leaves a remainder zero for all numbers.
HCF of 361, 209 is 19 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 361, 209 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 361, 209 is 19.
HCF(361, 209) = 19
HCF of 361, 209 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 361, 209 is 19.
Highest Common Factor of 361,209 is 19
Step 1: Since 361 > 209, we apply the division lemma to 361 and 209, to get
361 = 209 x 1 + 152
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 152 and 209, to get
209 = 152 x 1 + 57
Step 3: We consider the new divisor 152 and the new remainder 57, and apply the division lemma to get
152 = 57 x 2 + 38
We consider the new divisor 57 and the new remainder 38,and apply the division lemma to get
57 = 38 x 1 + 19
We consider the new divisor 38 and the new remainder 19,and apply the division lemma to get
38 = 19 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 361 and 209 is 19
Notice that 19 = HCF(38,19) = HCF(57,38) = HCF(152,57) = HCF(209,152) = HCF(361,209) .
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Frequently Asked Questions on HCF of 361, 209 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 361, 209?
Answer: HCF of 361, 209 is 19 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 361, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 361, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.