Highest Common Factor of 999, 573, 785 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 999, 573, 785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 999, 573, 785 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 999, 573, 785 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 999, 573, 785 is 1.

HCF(999, 573, 785) = 1

HCF of 999, 573, 785 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 999, 573, 785 is 1.

Highest Common Factor of 999,573,785 using Euclid's algorithm

Highest Common Factor of 999,573,785 is 1

Step 1: Since 999 > 573, we apply the division lemma to 999 and 573, to get

999 = 573 x 1 + 426

Step 2: Since the reminder 573 ≠ 0, we apply division lemma to 426 and 573, to get

573 = 426 x 1 + 147

Step 3: We consider the new divisor 426 and the new remainder 147, and apply the division lemma to get

426 = 147 x 2 + 132

We consider the new divisor 147 and the new remainder 132,and apply the division lemma to get

147 = 132 x 1 + 15

We consider the new divisor 132 and the new remainder 15,and apply the division lemma to get

132 = 15 x 8 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 999 and 573 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(132,15) = HCF(147,132) = HCF(426,147) = HCF(573,426) = HCF(999,573) .

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

Step 1: Since 785 > 3, we apply the division lemma to 785 and 3, to get

785 = 3 x 261 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 785 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(785,3) .

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Frequently Asked Questions on HCF of 999, 573, 785 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 999, 573, 785?

Answer: HCF of 999, 573, 785 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 999, 573, 785 using Euclid's Algorithm?

Answer: For arbitrary numbers 999, 573, 785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.