Highest Common Factor of 990, 8512 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 990, 8512 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 8512 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 990, 8512 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 990, 8512 is 2.
HCF(990, 8512) = 2
HCF of 990, 8512 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 8512 is 2.
Highest Common Factor of 990,8512 is 2
Step 1: Since 8512 > 990, we apply the division lemma to 8512 and 990, to get
8512 = 990 x 8 + 592
Step 2: Since the reminder 990 ≠ 0, we apply division lemma to 592 and 990, to get
990 = 592 x 1 + 398
Step 3: We consider the new divisor 592 and the new remainder 398, and apply the division lemma to get
592 = 398 x 1 + 194
We consider the new divisor 398 and the new remainder 194,and apply the division lemma to get
398 = 194 x 2 + 10
We consider the new divisor 194 and the new remainder 10,and apply the division lemma to get
194 = 10 x 19 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 990 and 8512 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(194,10) = HCF(398,194) = HCF(592,398) = HCF(990,592) = HCF(8512,990) .
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Frequently Asked Questions on HCF of 990, 8512 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 990, 8512?
Answer: HCF of 990, 8512 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 8512 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 8512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.