Highest Common Factor of 742, 448, 649 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 742, 448, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 742, 448, 649 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 742, 448, 649 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 742, 448, 649 is 1.

HCF(742, 448, 649) = 1

HCF of 742, 448, 649 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 742, 448, 649 is 1.

Highest Common Factor of 742,448,649 using Euclid's algorithm

Highest Common Factor of 742,448,649 is 1

Step 1: Since 742 > 448, we apply the division lemma to 742 and 448, to get

742 = 448 x 1 + 294

Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 294 and 448, to get

448 = 294 x 1 + 154

Step 3: We consider the new divisor 294 and the new remainder 154, and apply the division lemma to get

294 = 154 x 1 + 140

We consider the new divisor 154 and the new remainder 140,and apply the division lemma to get

154 = 140 x 1 + 14

We consider the new divisor 140 and the new remainder 14,and apply the division lemma to get

140 = 14 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 742 and 448 is 14

Notice that 14 = HCF(140,14) = HCF(154,140) = HCF(294,154) = HCF(448,294) = HCF(742,448) .

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

Step 1: Since 649 > 14, we apply the division lemma to 649 and 14, to get

649 = 14 x 46 + 5

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 5 and 14, to get

14 = 5 x 2 + 4

Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 649 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(649,14) .

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Frequently Asked Questions on HCF of 742, 448, 649 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 742, 448, 649?

Answer: HCF of 742, 448, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 742, 448, 649 using Euclid's Algorithm?

Answer: For arbitrary numbers 742, 448, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.