Highest Common Factor of 7680, 830 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 7680, 830 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 7680, 830 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 7680, 830 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 7680, 830 is 10.
HCF(7680, 830) = 10
HCF of 7680, 830 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7680, 830 is 10.
Highest Common Factor of 7680,830 is 10
Step 1: Since 7680 > 830, we apply the division lemma to 7680 and 830, to get
7680 = 830 x 9 + 210
Step 2: Since the reminder 830 ≠ 0, we apply division lemma to 210 and 830, to get
830 = 210 x 3 + 200
Step 3: We consider the new divisor 210 and the new remainder 200, and apply the division lemma to get
210 = 200 x 1 + 10
We consider the new divisor 200 and the new remainder 10, and apply the division lemma to get
200 = 10 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 7680 and 830 is 10
Notice that 10 = HCF(200,10) = HCF(210,200) = HCF(830,210) = HCF(7680,830) .
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Frequently Asked Questions on HCF of 7680, 830 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 7680, 830?
Answer: HCF of 7680, 830 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7680, 830 using Euclid's Algorithm?
Answer: For arbitrary numbers 7680, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.