Highest Common Factor of 774, 486, 332 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 774, 486, 332 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 774, 486, 332 is 2 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 774, 486, 332 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 774, 486, 332 is 2.

HCF(774, 486, 332) = 2

HCF of 774, 486, 332 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 774, 486, 332 is 2.

Highest Common Factor of 774,486,332 using Euclid's algorithm

Highest Common Factor of 774,486,332 is 2

Step 1: Since 774 > 486, we apply the division lemma to 774 and 486, to get

774 = 486 x 1 + 288

Step 2: Since the reminder 486 ≠ 0, we apply division lemma to 288 and 486, to get

486 = 288 x 1 + 198

Step 3: We consider the new divisor 288 and the new remainder 198, and apply the division lemma to get

288 = 198 x 1 + 90

We consider the new divisor 198 and the new remainder 90,and apply the division lemma to get

198 = 90 x 2 + 18

We consider the new divisor 90 and the new remainder 18,and apply the division lemma to get

90 = 18 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 774 and 486 is 18

Notice that 18 = HCF(90,18) = HCF(198,90) = HCF(288,198) = HCF(486,288) = HCF(774,486) .

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

Step 1: Since 332 > 18, we apply the division lemma to 332 and 18, to get

332 = 18 x 18 + 8

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 8 and 18, to get

18 = 8 x 2 + 2

Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 332 is 2

Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(332,18) .

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Frequently Asked Questions on HCF of 774, 486, 332 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 774, 486, 332?

Answer: HCF of 774, 486, 332 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 774, 486, 332 using Euclid's Algorithm?

Answer: For arbitrary numbers 774, 486, 332 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.