Highest Common Factor of 351, 598, 999 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 351, 598, 999 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 351, 598, 999 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 351, 598, 999 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 351, 598, 999 is 1.

HCF(351, 598, 999) = 1

HCF of 351, 598, 999 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 351, 598, 999 is 1.

Highest Common Factor of 351,598,999 using Euclid's algorithm

Highest Common Factor of 351,598,999 is 1

Step 1: Since 598 > 351, we apply the division lemma to 598 and 351, to get

598 = 351 x 1 + 247

Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 247 and 351, to get

351 = 247 x 1 + 104

Step 3: We consider the new divisor 247 and the new remainder 104, and apply the division lemma to get

247 = 104 x 2 + 39

We consider the new divisor 104 and the new remainder 39,and apply the division lemma to get

104 = 39 x 2 + 26

We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get

39 = 26 x 1 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 351 and 598 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(104,39) = HCF(247,104) = HCF(351,247) = HCF(598,351) .

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

Step 1: Since 999 > 13, we apply the division lemma to 999 and 13, to get

999 = 13 x 76 + 11

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 11 and 13, to get

13 = 11 x 1 + 2

Step 3: We consider the new divisor 11 and the new remainder 2, and apply the division lemma to get

11 = 2 x 5 + 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 13 and 999 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(999,13) .

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Frequently Asked Questions on HCF of 351, 598, 999 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 351, 598, 999?

Answer: HCF of 351, 598, 999 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 351, 598, 999 using Euclid's Algorithm?

Answer: For arbitrary numbers 351, 598, 999 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.