Highest Common Factor of 900, 702, 401 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, 702, 401 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 702, 401 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, 702, 401 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, 702, 401 is 1.

HCF(900, 702, 401) = 1

HCF of 900, 702, 401 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, 702, 401 is 1.

Highest Common Factor of 900,702,401 using Euclid's algorithm

Highest Common Factor of 900,702,401 is 1

Step 1: Since 900 > 702, we apply the division lemma to 900 and 702, to get

900 = 702 x 1 + 198

Step 2: Since the reminder 702 ≠ 0, we apply division lemma to 198 and 702, to get

702 = 198 x 3 + 108

Step 3: We consider the new divisor 198 and the new remainder 108, and apply the division lemma to get

198 = 108 x 1 + 90

We consider the new divisor 108 and the new remainder 90,and apply the division lemma to get

108 = 90 x 1 + 18

We consider the new divisor 90 and the new remainder 18,and apply the division lemma to get

90 = 18 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 900 and 702 is 18

Notice that 18 = HCF(90,18) = HCF(108,90) = HCF(198,108) = HCF(702,198) = HCF(900,702) .

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

Step 1: Since 401 > 18, we apply the division lemma to 401 and 18, to get

401 = 18 x 22 + 5

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 5 and 18, to get

18 = 5 x 3 + 3

Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 18 and 401 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(401,18) .

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Frequently Asked Questions on HCF of 900, 702, 401 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, 702, 401?

Answer: HCF of 900, 702, 401 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 702, 401 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 702, 401 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.