Highest Common Factor of 998, 382, 320 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, 382, 320 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 382, 320 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 998, 382, 320 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, 382, 320 is 2.
HCF(998, 382, 320) = 2
HCF of 998, 382, 320 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, 382, 320 is 2.
Highest Common Factor of 998,382,320 is 2
Step 1: Since 998 > 382, we apply the division lemma to 998 and 382, to get
998 = 382 x 2 + 234
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 234 and 382, to get
382 = 234 x 1 + 148
Step 3: We consider the new divisor 234 and the new remainder 148, and apply the division lemma to get
234 = 148 x 1 + 86
We consider the new divisor 148 and the new remainder 86,and apply the division lemma to get
148 = 86 x 1 + 62
We consider the new divisor 86 and the new remainder 62,and apply the division lemma to get
86 = 62 x 1 + 24
We consider the new divisor 62 and the new remainder 24,and apply the division lemma to get
62 = 24 x 2 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 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 998 and 382 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(62,24) = HCF(86,62) = HCF(148,86) = HCF(234,148) = HCF(382,234) = HCF(998,382) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 320 > 2, we apply the division lemma to 320 and 2, to get
320 = 2 x 160 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 320 is 2
Notice that 2 = HCF(320,2) .
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Frequently Asked Questions on HCF of 998, 382, 320 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, 382, 320?
Answer: HCF of 998, 382, 320 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 382, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 382, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.