Highest Common Factor of 1642, 8896, 25996 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 1642, 8896, 25996 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1642, 8896, 25996 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 1642, 8896, 25996 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 1642, 8896, 25996 is 2.
HCF(1642, 8896, 25996) = 2
HCF of 1642, 8896, 25996 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1642, 8896, 25996 is 2.
Highest Common Factor of 1642,8896,25996 is 2
Step 1: Since 8896 > 1642, we apply the division lemma to 8896 and 1642, to get
8896 = 1642 x 5 + 686
Step 2: Since the reminder 1642 ≠ 0, we apply division lemma to 686 and 1642, to get
1642 = 686 x 2 + 270
Step 3: We consider the new divisor 686 and the new remainder 270, and apply the division lemma to get
686 = 270 x 2 + 146
We consider the new divisor 270 and the new remainder 146,and apply the division lemma to get
270 = 146 x 1 + 124
We consider the new divisor 146 and the new remainder 124,and apply the division lemma to get
146 = 124 x 1 + 22
We consider the new divisor 124 and the new remainder 22,and apply the division lemma to get
124 = 22 x 5 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1642 and 8896 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(124,22) = HCF(146,124) = HCF(270,146) = HCF(686,270) = HCF(1642,686) = HCF(8896,1642) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 25996 > 2, we apply the division lemma to 25996 and 2, to get
25996 = 2 x 12998 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 25996 is 2
Notice that 2 = HCF(25996,2) .
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Frequently Asked Questions on HCF of 1642, 8896, 25996 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 1642, 8896, 25996?
Answer: HCF of 1642, 8896, 25996 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1642, 8896, 25996 using Euclid's Algorithm?
Answer: For arbitrary numbers 1642, 8896, 25996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.