Highest Common Factor of 825, 1043 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 825, 1043 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 1043 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 825, 1043 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 825, 1043 is 1.
HCF(825, 1043) = 1
HCF of 825, 1043 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 825, 1043 is 1.
Highest Common Factor of 825,1043 is 1
Step 1: Since 1043 > 825, we apply the division lemma to 1043 and 825, to get
1043 = 825 x 1 + 218
Step 2: Since the reminder 825 ≠ 0, we apply division lemma to 218 and 825, to get
825 = 218 x 3 + 171
Step 3: We consider the new divisor 218 and the new remainder 171, and apply the division lemma to get
218 = 171 x 1 + 47
We consider the new divisor 171 and the new remainder 47,and apply the division lemma to get
171 = 47 x 3 + 30
We consider the new divisor 47 and the new remainder 30,and apply the division lemma to get
47 = 30 x 1 + 17
We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get
30 = 17 x 1 + 13
We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get
17 = 13 x 1 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 825 and 1043 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(47,30) = HCF(171,47) = HCF(218,171) = HCF(825,218) = HCF(1043,825) .
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Frequently Asked Questions on HCF of 825, 1043 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 825, 1043?
Answer: HCF of 825, 1043 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 1043 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 1043 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
