Highest Common Factor of 8738, 8904 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 8738, 8904 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8738, 8904 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 8738, 8904 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 8738, 8904 is 2.
HCF(8738, 8904) = 2
HCF of 8738, 8904 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8738, 8904 is 2.
Highest Common Factor of 8738,8904 is 2
Step 1: Since 8904 > 8738, we apply the division lemma to 8904 and 8738, to get
8904 = 8738 x 1 + 166
Step 2: Since the reminder 8738 ≠ 0, we apply division lemma to 166 and 8738, to get
8738 = 166 x 52 + 106
Step 3: We consider the new divisor 166 and the new remainder 106, and apply the division lemma to get
166 = 106 x 1 + 60
We consider the new divisor 106 and the new remainder 60,and apply the division lemma to get
106 = 60 x 1 + 46
We consider the new divisor 60 and the new remainder 46,and apply the division lemma to get
60 = 46 x 1 + 14
We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get
46 = 14 x 3 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 8738 and 8904 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(60,46) = HCF(106,60) = HCF(166,106) = HCF(8738,166) = HCF(8904,8738) .
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Frequently Asked Questions on HCF of 8738, 8904 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 8738, 8904?
Answer: HCF of 8738, 8904 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8738, 8904 using Euclid's Algorithm?
Answer: For arbitrary numbers 8738, 8904 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.