Highest Common Factor of 900, 373, 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 900, 373, 300 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 373, 300 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 900, 373, 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 900, 373, 300 is 1.

HCF(900, 373, 300) = 1

HCF of 900, 373, 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 900, 373, 300 is 1.

Highest Common Factor of 900,373,300 using Euclid's algorithm

Highest Common Factor of 900,373,300 is 1

Step 1: Since 900 > 373, we apply the division lemma to 900 and 373, to get

900 = 373 x 2 + 154

Step 2: Since the reminder 373 ≠ 0, we apply division lemma to 154 and 373, to get

373 = 154 x 2 + 65

Step 3: We consider the new divisor 154 and the new remainder 65, and apply the division lemma to get

154 = 65 x 2 + 24

We consider the new divisor 65 and the new remainder 24,and apply the division lemma to get

65 = 24 x 2 + 17

We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get

24 = 17 x 1 + 7

We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get

17 = 7 x 2 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 900 and 373 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(65,24) = HCF(154,65) = HCF(373,154) = HCF(900,373) .

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

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

300 = 1 x 300 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 300 is 1

Notice that 1 = HCF(300,1) .

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Frequently Asked Questions on HCF of 900, 373, 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 900, 373, 300?

Answer: HCF of 900, 373, 300 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 373, 300 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 373, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.