Highest Common Factor of 990, 277, 103 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, 277, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 990, 277, 103 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, 277, 103 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, 277, 103 is 1.

HCF(990, 277, 103) = 1

HCF of 990, 277, 103 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 990, 277, 103 is 1.

Highest Common Factor of 990,277,103 using Euclid's algorithm

Highest Common Factor of 990,277,103 is 1

Step 1: Since 990 > 277, we apply the division lemma to 990 and 277, to get

990 = 277 x 3 + 159

Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 159 and 277, to get

277 = 159 x 1 + 118

Step 3: We consider the new divisor 159 and the new remainder 118, and apply the division lemma to get

159 = 118 x 1 + 41

We consider the new divisor 118 and the new remainder 41,and apply the division lemma to get

118 = 41 x 2 + 36

We consider the new divisor 41 and the new remainder 36,and apply the division lemma to get

41 = 36 x 1 + 5

We consider the new divisor 36 and the new remainder 5,and apply the division lemma to get

36 = 5 x 7 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 990 and 277 is 1

Notice that 1 = HCF(5,1) = HCF(36,5) = HCF(41,36) = HCF(118,41) = HCF(159,118) = HCF(277,159) = HCF(990,277) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get

103 = 1 x 103 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1

Notice that 1 = HCF(103,1) .

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Frequently Asked Questions on HCF of 990, 277, 103 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, 277, 103?

Answer: HCF of 990, 277, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 990, 277, 103 using Euclid's Algorithm?

Answer: For arbitrary numbers 990, 277, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.