Highest Common Factor of 649, 885, 723 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 649, 885, 723 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 649, 885, 723 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 649, 885, 723 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 649, 885, 723 is 1.

HCF(649, 885, 723) = 1

HCF of 649, 885, 723 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 649, 885, 723 is 1.

Highest Common Factor of 649,885,723 using Euclid's algorithm

Highest Common Factor of 649,885,723 is 1

Step 1: Since 885 > 649, we apply the division lemma to 885 and 649, to get

885 = 649 x 1 + 236

Step 2: Since the reminder 649 ≠ 0, we apply division lemma to 236 and 649, to get

649 = 236 x 2 + 177

Step 3: We consider the new divisor 236 and the new remainder 177, and apply the division lemma to get

236 = 177 x 1 + 59

We consider the new divisor 177 and the new remainder 59, and apply the division lemma to get

177 = 59 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 649 and 885 is 59

Notice that 59 = HCF(177,59) = HCF(236,177) = HCF(649,236) = HCF(885,649) .

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

Step 1: Since 723 > 59, we apply the division lemma to 723 and 59, to get

723 = 59 x 12 + 15

Step 2: Since the reminder 59 ≠ 0, we apply division lemma to 15 and 59, to get

59 = 15 x 3 + 14

Step 3: We consider the new divisor 15 and the new remainder 14, and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1, and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 59 and 723 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(59,15) = HCF(723,59) .

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Frequently Asked Questions on HCF of 649, 885, 723 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 649, 885, 723?

Answer: HCF of 649, 885, 723 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 649, 885, 723 using Euclid's Algorithm?

Answer: For arbitrary numbers 649, 885, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.