Highest Common Factor of 826, 8004 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 826, 8004 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 826, 8004 is 2 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 826, 8004 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 826, 8004 is 2.
HCF(826, 8004) = 2
HCF of 826, 8004 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 826, 8004 is 2.
Highest Common Factor of 826,8004 is 2
Step 1: Since 8004 > 826, we apply the division lemma to 8004 and 826, to get
8004 = 826 x 9 + 570
Step 2: Since the reminder 826 ≠ 0, we apply division lemma to 570 and 826, to get
826 = 570 x 1 + 256
Step 3: We consider the new divisor 570 and the new remainder 256, and apply the division lemma to get
570 = 256 x 2 + 58
We consider the new divisor 256 and the new remainder 58,and apply the division lemma to get
256 = 58 x 4 + 24
We consider the new divisor 58 and the new remainder 24,and apply the division lemma to get
58 = 24 x 2 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 826 and 8004 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(58,24) = HCF(256,58) = HCF(570,256) = HCF(826,570) = HCF(8004,826) .
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Frequently Asked Questions on HCF of 826, 8004 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 826, 8004?
Answer: HCF of 826, 8004 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 826, 8004 using Euclid's Algorithm?
Answer: For arbitrary numbers 826, 8004 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.