Highest Common Factor of 990, 272, 331 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, 272, 331 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 272, 331 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 990, 272, 331 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, 272, 331 is 1.
HCF(990, 272, 331) = 1
HCF of 990, 272, 331 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, 272, 331 is 1.
Highest Common Factor of 990,272,331 is 1
Step 1: Since 990 > 272, we apply the division lemma to 990 and 272, to get
990 = 272 x 3 + 174
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 174 and 272, to get
272 = 174 x 1 + 98
Step 3: We consider the new divisor 174 and the new remainder 98, and apply the division lemma to get
174 = 98 x 1 + 76
We consider the new divisor 98 and the new remainder 76,and apply the division lemma to get
98 = 76 x 1 + 22
We consider the new divisor 76 and the new remainder 22,and apply the division lemma to get
76 = 22 x 3 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 990 and 272 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(76,22) = HCF(98,76) = HCF(174,98) = HCF(272,174) = HCF(990,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 331 > 2, we apply the division lemma to 331 and 2, to get
331 = 2 x 165 + 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 331 is 1
Notice that 1 = HCF(2,1) = HCF(331,2) .
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Frequently Asked Questions on HCF of 990, 272, 331 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, 272, 331?
Answer: HCF of 990, 272, 331 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 272, 331 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 272, 331 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.