Highest Common Factor of 9825, 6746 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 9825, 6746 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9825, 6746 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 9825, 6746 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 9825, 6746 is 1.
HCF(9825, 6746) = 1
HCF of 9825, 6746 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9825, 6746 is 1.
Highest Common Factor of 9825,6746 is 1
Step 1: Since 9825 > 6746, we apply the division lemma to 9825 and 6746, to get
9825 = 6746 x 1 + 3079
Step 2: Since the reminder 6746 ≠ 0, we apply division lemma to 3079 and 6746, to get
6746 = 3079 x 2 + 588
Step 3: We consider the new divisor 3079 and the new remainder 588, and apply the division lemma to get
3079 = 588 x 5 + 139
We consider the new divisor 588 and the new remainder 139,and apply the division lemma to get
588 = 139 x 4 + 32
We consider the new divisor 139 and the new remainder 32,and apply the division lemma to get
139 = 32 x 4 + 11
We consider the new divisor 32 and the new remainder 11,and apply the division lemma to get
32 = 11 x 2 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9825 and 6746 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(32,11) = HCF(139,32) = HCF(588,139) = HCF(3079,588) = HCF(6746,3079) = HCF(9825,6746) .
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Frequently Asked Questions on HCF of 9825, 6746 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 9825, 6746?
Answer: HCF of 9825, 6746 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9825, 6746 using Euclid's Algorithm?
Answer: For arbitrary numbers 9825, 6746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.