Highest Common Factor of 1000, 7830 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 1000, 7830 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 1000, 7830 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 1000, 7830 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 1000, 7830 is 10.
HCF(1000, 7830) = 10
HCF of 1000, 7830 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1000, 7830 is 10.
Highest Common Factor of 1000,7830 is 10
Step 1: Since 7830 > 1000, we apply the division lemma to 7830 and 1000, to get
7830 = 1000 x 7 + 830
Step 2: Since the reminder 1000 ≠ 0, we apply division lemma to 830 and 1000, to get
1000 = 830 x 1 + 170
Step 3: We consider the new divisor 830 and the new remainder 170, and apply the division lemma to get
830 = 170 x 4 + 150
We consider the new divisor 170 and the new remainder 150,and apply the division lemma to get
170 = 150 x 1 + 20
We consider the new divisor 150 and the new remainder 20,and apply the division lemma to get
150 = 20 x 7 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 1000 and 7830 is 10
Notice that 10 = HCF(20,10) = HCF(150,20) = HCF(170,150) = HCF(830,170) = HCF(1000,830) = HCF(7830,1000) .
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Frequently Asked Questions on HCF of 1000, 7830 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 1000, 7830?
Answer: HCF of 1000, 7830 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1000, 7830 using Euclid's Algorithm?
Answer: For arbitrary numbers 1000, 7830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.