Highest Common Factor of 998, 906, 743 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, 906, 743 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 906, 743 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, 906, 743 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, 906, 743 is 1.
HCF(998, 906, 743) = 1
HCF of 998, 906, 743 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, 906, 743 is 1.
Highest Common Factor of 998,906,743 is 1
Step 1: Since 998 > 906, we apply the division lemma to 998 and 906, to get
998 = 906 x 1 + 92
Step 2: Since the reminder 906 ≠ 0, we apply division lemma to 92 and 906, to get
906 = 92 x 9 + 78
Step 3: We consider the new divisor 92 and the new remainder 78, and apply the division lemma to get
92 = 78 x 1 + 14
We consider the new divisor 78 and the new remainder 14,and apply the division lemma to get
78 = 14 x 5 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 906 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(78,14) = HCF(92,78) = HCF(906,92) = HCF(998,906) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 743 > 2, we apply the division lemma to 743 and 2, to get
743 = 2 x 371 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 743 is 1
Notice that 1 = HCF(2,1) = HCF(743,2) .
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Frequently Asked Questions on HCF of 998, 906, 743 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, 906, 743?
Answer: HCF of 998, 906, 743 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 906, 743 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 906, 743 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.