Highest Common Factor of 333, 555, 357, 68 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 333, 555, 357, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 333, 555, 357, 68 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 333, 555, 357, 68 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 333, 555, 357, 68 is 1.

HCF(333, 555, 357, 68) = 1

HCF of 333, 555, 357, 68 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 333, 555, 357, 68 is 1.

Highest Common Factor of 333,555,357,68 using Euclid's algorithm

Highest Common Factor of 333,555,357,68 is 1

Step 1: Since 555 > 333, we apply the division lemma to 555 and 333, to get

555 = 333 x 1 + 222

Step 2: Since the reminder 333 ≠ 0, we apply division lemma to 222 and 333, to get

333 = 222 x 1 + 111

Step 3: We consider the new divisor 222 and the new remainder 111, and apply the division lemma to get

222 = 111 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 111, the HCF of 333 and 555 is 111

Notice that 111 = HCF(222,111) = HCF(333,222) = HCF(555,333) .

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

Step 1: Since 357 > 111, we apply the division lemma to 357 and 111, to get

357 = 111 x 3 + 24

Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 24 and 111, to get

111 = 24 x 4 + 15

Step 3: We consider the new divisor 24 and the new remainder 15, and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 111 and 357 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(111,24) = HCF(357,111) .

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

Step 1: Since 68 > 3, we apply the division lemma to 68 and 3, to get

68 = 3 x 22 + 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 68 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(68,3) .

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Frequently Asked Questions on HCF of 333, 555, 357, 68 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 333, 555, 357, 68?

Answer: HCF of 333, 555, 357, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 333, 555, 357, 68 using Euclid's Algorithm?

Answer: For arbitrary numbers 333, 555, 357, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.