Highest Common Factor of 450, 774, 133 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 450, 774, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 774, 133 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 450, 774, 133 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 450, 774, 133 is 1.

HCF(450, 774, 133) = 1

HCF of 450, 774, 133 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 450, 774, 133 is 1.

Highest Common Factor of 450,774,133 using Euclid's algorithm

Highest Common Factor of 450,774,133 is 1

Step 1: Since 774 > 450, we apply the division lemma to 774 and 450, to get

774 = 450 x 1 + 324

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 324 and 450, to get

450 = 324 x 1 + 126

Step 3: We consider the new divisor 324 and the new remainder 126, and apply the division lemma to get

324 = 126 x 2 + 72

We consider the new divisor 126 and the new remainder 72,and apply the division lemma to get

126 = 72 x 1 + 54

We consider the new divisor 72 and the new remainder 54,and apply the division lemma to get

72 = 54 x 1 + 18

We consider the new divisor 54 and the new remainder 18,and apply the division lemma to get

54 = 18 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 450 and 774 is 18

Notice that 18 = HCF(54,18) = HCF(72,54) = HCF(126,72) = HCF(324,126) = HCF(450,324) = HCF(774,450) .

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

Step 1: Since 133 > 18, we apply the division lemma to 133 and 18, to get

133 = 18 x 7 + 7

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 7 and 18, to get

18 = 7 x 2 + 4

Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 18 and 133 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(133,18) .

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Frequently Asked Questions on HCF of 450, 774, 133 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 450, 774, 133?

Answer: HCF of 450, 774, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 774, 133 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 774, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.