Highest Common Factor of 749, 7296, 3485 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 749, 7296, 3485 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 749, 7296, 3485 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 749, 7296, 3485 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 749, 7296, 3485 is 1.

HCF(749, 7296, 3485) = 1

HCF of 749, 7296, 3485 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 749, 7296, 3485 is 1.

Highest Common Factor of 749,7296,3485 using Euclid's algorithm

Highest Common Factor of 749,7296,3485 is 1

Step 1: Since 7296 > 749, we apply the division lemma to 7296 and 749, to get

7296 = 749 x 9 + 555

Step 2: Since the reminder 749 ≠ 0, we apply division lemma to 555 and 749, to get

749 = 555 x 1 + 194

Step 3: We consider the new divisor 555 and the new remainder 194, and apply the division lemma to get

555 = 194 x 2 + 167

We consider the new divisor 194 and the new remainder 167,and apply the division lemma to get

194 = 167 x 1 + 27

We consider the new divisor 167 and the new remainder 27,and apply the division lemma to get

167 = 27 x 6 + 5

We consider the new divisor 27 and the new remainder 5,and apply the division lemma to get

27 = 5 x 5 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

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 749 and 7296 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(167,27) = HCF(194,167) = HCF(555,194) = HCF(749,555) = HCF(7296,749) .

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

Step 1: Since 3485 > 1, we apply the division lemma to 3485 and 1, to get

3485 = 1 x 3485 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3485 is 1

Notice that 1 = HCF(3485,1) .

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Frequently Asked Questions on HCF of 749, 7296, 3485 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 749, 7296, 3485?

Answer: HCF of 749, 7296, 3485 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 749, 7296, 3485 using Euclid's Algorithm?

Answer: For arbitrary numbers 749, 7296, 3485 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.