Highest Common Factor of 209, 319 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 209, 319 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 319 is 11 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 209, 319 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 209, 319 is 11.
HCF(209, 319) = 11
HCF of 209, 319 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 319 is 11.
Highest Common Factor of 209,319 is 11
Step 1: Since 319 > 209, we apply the division lemma to 319 and 209, to get
319 = 209 x 1 + 110
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 110 and 209, to get
209 = 110 x 1 + 99
Step 3: We consider the new divisor 110 and the new remainder 99, and apply the division lemma to get
110 = 99 x 1 + 11
We consider the new divisor 99 and the new remainder 11, and apply the division lemma to get
99 = 11 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 209 and 319 is 11
Notice that 11 = HCF(99,11) = HCF(110,99) = HCF(209,110) = HCF(319,209) .
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Frequently Asked Questions on HCF of 209, 319 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 209, 319?
Answer: HCF of 209, 319 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 319 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 319 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.