Highest Common Factor of 1805, 9705 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 1805, 9705 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 1805, 9705 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 1805, 9705 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 1805, 9705 is 5.
HCF(1805, 9705) = 5
HCF of 1805, 9705 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1805, 9705 is 5.
Highest Common Factor of 1805,9705 is 5
Step 1: Since 9705 > 1805, we apply the division lemma to 9705 and 1805, to get
9705 = 1805 x 5 + 680
Step 2: Since the reminder 1805 ≠ 0, we apply division lemma to 680 and 1805, to get
1805 = 680 x 2 + 445
Step 3: We consider the new divisor 680 and the new remainder 445, and apply the division lemma to get
680 = 445 x 1 + 235
We consider the new divisor 445 and the new remainder 235,and apply the division lemma to get
445 = 235 x 1 + 210
We consider the new divisor 235 and the new remainder 210,and apply the division lemma to get
235 = 210 x 1 + 25
We consider the new divisor 210 and the new remainder 25,and apply the division lemma to get
210 = 25 x 8 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 1805 and 9705 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(210,25) = HCF(235,210) = HCF(445,235) = HCF(680,445) = HCF(1805,680) = HCF(9705,1805) .
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Frequently Asked Questions on HCF of 1805, 9705 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 1805, 9705?
Answer: HCF of 1805, 9705 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1805, 9705 using Euclid's Algorithm?
Answer: For arbitrary numbers 1805, 9705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.