Highest Common Factor of 990, 356, 300 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, 356, 300 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 990, 356, 300 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 990, 356, 300 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, 356, 300 is 2.

HCF(990, 356, 300) = 2

HCF of 990, 356, 300 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, 356, 300 is 2.

Highest Common Factor of 990,356,300 using Euclid's algorithm

Highest Common Factor of 990,356,300 is 2

Step 1: Since 990 > 356, we apply the division lemma to 990 and 356, to get

990 = 356 x 2 + 278

Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 278 and 356, to get

356 = 278 x 1 + 78

Step 3: We consider the new divisor 278 and the new remainder 78, and apply the division lemma to get

278 = 78 x 3 + 44

We consider the new divisor 78 and the new remainder 44,and apply the division lemma to get

78 = 44 x 1 + 34

We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get

44 = 34 x 1 + 10

We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get

34 = 10 x 3 + 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 990 and 356 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(78,44) = HCF(278,78) = HCF(356,278) = HCF(990,356) .

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

Step 1: Since 300 > 2, we apply the division lemma to 300 and 2, to get

300 = 2 x 150 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 300 is 2

Notice that 2 = HCF(300,2) .

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Frequently Asked Questions on HCF of 990, 356, 300 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, 356, 300?

Answer: HCF of 990, 356, 300 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 990, 356, 300 using Euclid's Algorithm?

Answer: For arbitrary numbers 990, 356, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.