Highest Common Factor of 7440, 8230 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 7440, 8230 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 7440, 8230 is 10 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 7440, 8230 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 7440, 8230 is 10.
HCF(7440, 8230) = 10
HCF of 7440, 8230 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7440, 8230 is 10.
Highest Common Factor of 7440,8230 is 10
Step 1: Since 8230 > 7440, we apply the division lemma to 8230 and 7440, to get
8230 = 7440 x 1 + 790
Step 2: Since the reminder 7440 ≠ 0, we apply division lemma to 790 and 7440, to get
7440 = 790 x 9 + 330
Step 3: We consider the new divisor 790 and the new remainder 330, and apply the division lemma to get
790 = 330 x 2 + 130
We consider the new divisor 330 and the new remainder 130,and apply the division lemma to get
330 = 130 x 2 + 70
We consider the new divisor 130 and the new remainder 70,and apply the division lemma to get
130 = 70 x 1 + 60
We consider the new divisor 70 and the new remainder 60,and apply the division lemma to get
70 = 60 x 1 + 10
We consider the new divisor 60 and the new remainder 10,and apply the division lemma to get
60 = 10 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 7440 and 8230 is 10
Notice that 10 = HCF(60,10) = HCF(70,60) = HCF(130,70) = HCF(330,130) = HCF(790,330) = HCF(7440,790) = HCF(8230,7440) .
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Frequently Asked Questions on HCF of 7440, 8230 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 7440, 8230?
Answer: HCF of 7440, 8230 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7440, 8230 using Euclid's Algorithm?
Answer: For arbitrary numbers 7440, 8230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.