Highest Common Factor of 549, 696, 446, 74 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 549, 696, 446, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 549, 696, 446, 74 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 549, 696, 446, 74 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 549, 696, 446, 74 is 1.

HCF(549, 696, 446, 74) = 1

HCF of 549, 696, 446, 74 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 549, 696, 446, 74 is 1.

Highest Common Factor of 549,696,446,74 using Euclid's algorithm

Highest Common Factor of 549,696,446,74 is 1

Step 1: Since 696 > 549, we apply the division lemma to 696 and 549, to get

696 = 549 x 1 + 147

Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 147 and 549, to get

549 = 147 x 3 + 108

Step 3: We consider the new divisor 147 and the new remainder 108, and apply the division lemma to get

147 = 108 x 1 + 39

We consider the new divisor 108 and the new remainder 39,and apply the division lemma to get

108 = 39 x 2 + 30

We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get

39 = 30 x 1 + 9

We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get

30 = 9 x 3 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 549 and 696 is 3

Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(108,39) = HCF(147,108) = HCF(549,147) = HCF(696,549) .

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

Step 1: Since 446 > 3, we apply the division lemma to 446 and 3, to get

446 = 3 x 148 + 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 446 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(446,3) .

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

Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get

74 = 1 x 74 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1

Notice that 1 = HCF(74,1) .

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Frequently Asked Questions on HCF of 549, 696, 446, 74 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 549, 696, 446, 74?

Answer: HCF of 549, 696, 446, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 549, 696, 446, 74 using Euclid's Algorithm?

Answer: For arbitrary numbers 549, 696, 446, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.