Highest Common Factor of 909, 2069 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 909, 2069 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 2069 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 909, 2069 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 909, 2069 is 1.
HCF(909, 2069) = 1
HCF of 909, 2069 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 909, 2069 is 1.
Highest Common Factor of 909,2069 is 1
Step 1: Since 2069 > 909, we apply the division lemma to 2069 and 909, to get
2069 = 909 x 2 + 251
Step 2: Since the reminder 909 ≠ 0, we apply division lemma to 251 and 909, to get
909 = 251 x 3 + 156
Step 3: We consider the new divisor 251 and the new remainder 156, and apply the division lemma to get
251 = 156 x 1 + 95
We consider the new divisor 156 and the new remainder 95,and apply the division lemma to get
156 = 95 x 1 + 61
We consider the new divisor 95 and the new remainder 61,and apply the division lemma to get
95 = 61 x 1 + 34
We consider the new divisor 61 and the new remainder 34,and apply the division lemma to get
61 = 34 x 1 + 27
We consider the new divisor 34 and the new remainder 27,and apply the division lemma to get
34 = 27 x 1 + 7
We consider the new divisor 27 and the new remainder 7,and apply the division lemma to get
27 = 7 x 3 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 909 and 2069 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(27,7) = HCF(34,27) = HCF(61,34) = HCF(95,61) = HCF(156,95) = HCF(251,156) = HCF(909,251) = HCF(2069,909) .
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Frequently Asked Questions on HCF of 909, 2069 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 909, 2069?
Answer: HCF of 909, 2069 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 2069 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 2069 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.