Highest Common Factor of 900, 353, 549, 690 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, 353, 549, 690 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 900, 353, 549, 690 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, 353, 549, 690 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, 353, 549, 690 is 1.

HCF(900, 353, 549, 690) = 1

HCF of 900, 353, 549, 690 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, 353, 549, 690 is 1.

Highest Common Factor of 900,353,549,690 using Euclid's algorithm

Highest Common Factor of 900,353,549,690 is 1

Step 1: Since 900 > 353, we apply the division lemma to 900 and 353, to get

900 = 353 x 2 + 194

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 194 and 353, to get

353 = 194 x 1 + 159

Step 3: We consider the new divisor 194 and the new remainder 159, and apply the division lemma to get

194 = 159 x 1 + 35

We consider the new divisor 159 and the new remainder 35,and apply the division lemma to get

159 = 35 x 4 + 19

We consider the new divisor 35 and the new remainder 19,and apply the division lemma to get

35 = 19 x 1 + 16

We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get

19 = 16 x 1 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 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 353 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(35,19) = HCF(159,35) = HCF(194,159) = HCF(353,194) = HCF(900,353) .

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

Step 1: Since 549 > 1, we apply the division lemma to 549 and 1, to get

549 = 1 x 549 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 549 is 1

Notice that 1 = HCF(549,1) .

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

Step 1: Since 690 > 1, we apply the division lemma to 690 and 1, to get

690 = 1 x 690 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 690 is 1

Notice that 1 = HCF(690,1) .

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Frequently Asked Questions on HCF of 900, 353, 549, 690 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, 353, 549, 690?

Answer: HCF of 900, 353, 549, 690 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 900, 353, 549, 690 using Euclid's Algorithm?

Answer: For arbitrary numbers 900, 353, 549, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.