Highest Common Factor of 2045, 9775 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 2045, 9775 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 2045, 9775 is 5 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 2045, 9775 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 2045, 9775 is 5.
HCF(2045, 9775) = 5
HCF of 2045, 9775 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2045, 9775 is 5.
Highest Common Factor of 2045,9775 is 5
Step 1: Since 9775 > 2045, we apply the division lemma to 9775 and 2045, to get
9775 = 2045 x 4 + 1595
Step 2: Since the reminder 2045 ≠ 0, we apply division lemma to 1595 and 2045, to get
2045 = 1595 x 1 + 450
Step 3: We consider the new divisor 1595 and the new remainder 450, and apply the division lemma to get
1595 = 450 x 3 + 245
We consider the new divisor 450 and the new remainder 245,and apply the division lemma to get
450 = 245 x 1 + 205
We consider the new divisor 245 and the new remainder 205,and apply the division lemma to get
245 = 205 x 1 + 40
We consider the new divisor 205 and the new remainder 40,and apply the division lemma to get
205 = 40 x 5 + 5
We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2045 and 9775 is 5
Notice that 5 = HCF(40,5) = HCF(205,40) = HCF(245,205) = HCF(450,245) = HCF(1595,450) = HCF(2045,1595) = HCF(9775,2045) .
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Frequently Asked Questions on HCF of 2045, 9775 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 2045, 9775?
Answer: HCF of 2045, 9775 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2045, 9775 using Euclid's Algorithm?
Answer: For arbitrary numbers 2045, 9775 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.