Highest Common Factor of 1030, 8670 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 1030, 8670 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 1030, 8670 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 1030, 8670 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 1030, 8670 is 10.
HCF(1030, 8670) = 10
HCF of 1030, 8670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1030, 8670 is 10.
Highest Common Factor of 1030,8670 is 10
Step 1: Since 8670 > 1030, we apply the division lemma to 8670 and 1030, to get
8670 = 1030 x 8 + 430
Step 2: Since the reminder 1030 ≠ 0, we apply division lemma to 430 and 1030, to get
1030 = 430 x 2 + 170
Step 3: We consider the new divisor 430 and the new remainder 170, and apply the division lemma to get
430 = 170 x 2 + 90
We consider the new divisor 170 and the new remainder 90,and apply the division lemma to get
170 = 90 x 1 + 80
We consider the new divisor 90 and the new remainder 80,and apply the division lemma to get
90 = 80 x 1 + 10
We consider the new divisor 80 and the new remainder 10,and apply the division lemma to get
80 = 10 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 1030 and 8670 is 10
Notice that 10 = HCF(80,10) = HCF(90,80) = HCF(170,90) = HCF(430,170) = HCF(1030,430) = HCF(8670,1030) .
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Frequently Asked Questions on HCF of 1030, 8670 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 1030, 8670?
Answer: HCF of 1030, 8670 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1030, 8670 using Euclid's Algorithm?
Answer: For arbitrary numbers 1030, 8670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.