Highest Common Factor of 668, 285, 303, 12 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 668, 285, 303, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 668, 285, 303, 12 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 668, 285, 303, 12 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 668, 285, 303, 12 is 1.

HCF(668, 285, 303, 12) = 1

HCF of 668, 285, 303, 12 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 668, 285, 303, 12 is 1.

Highest Common Factor of 668,285,303,12 using Euclid's algorithm

Highest Common Factor of 668,285,303,12 is 1

Step 1: Since 668 > 285, we apply the division lemma to 668 and 285, to get

668 = 285 x 2 + 98

Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 98 and 285, to get

285 = 98 x 2 + 89

Step 3: We consider the new divisor 98 and the new remainder 89, and apply the division lemma to get

98 = 89 x 1 + 9

We consider the new divisor 89 and the new remainder 9,and apply the division lemma to get

89 = 9 x 9 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 668 and 285 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(89,9) = HCF(98,89) = HCF(285,98) = HCF(668,285) .

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

Step 1: Since 303 > 1, we apply the division lemma to 303 and 1, to get

303 = 1 x 303 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 303 is 1

Notice that 1 = HCF(303,1) .

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

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

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Frequently Asked Questions on HCF of 668, 285, 303, 12 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 668, 285, 303, 12?

Answer: HCF of 668, 285, 303, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 668, 285, 303, 12 using Euclid's Algorithm?

Answer: For arbitrary numbers 668, 285, 303, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.