Highest Common Factor of 998, 16047 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 998, 16047 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 16047 is 1 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 998, 16047 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 998, 16047 is 1.
HCF(998, 16047) = 1
HCF of 998, 16047 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 998, 16047 is 1.
Highest Common Factor of 998,16047 is 1
Step 1: Since 16047 > 998, we apply the division lemma to 16047 and 998, to get
16047 = 998 x 16 + 79
Step 2: Since the reminder 998 ≠ 0, we apply division lemma to 79 and 998, to get
998 = 79 x 12 + 50
Step 3: We consider the new divisor 79 and the new remainder 50, and apply the division lemma to get
79 = 50 x 1 + 29
We consider the new divisor 50 and the new remainder 29,and apply the division lemma to get
50 = 29 x 1 + 21
We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get
29 = 21 x 1 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 998 and 16047 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(50,29) = HCF(79,50) = HCF(998,79) = HCF(16047,998) .
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Frequently Asked Questions on HCF of 998, 16047 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 998, 16047?
Answer: HCF of 998, 16047 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 16047 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 16047 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.