Highest Common Factor of 752, 480, 699 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 752, 480, 699 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 752, 480, 699 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 752, 480, 699 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 752, 480, 699 is 1.

HCF(752, 480, 699) = 1

HCF of 752, 480, 699 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 752, 480, 699 is 1.

Highest Common Factor of 752,480,699 using Euclid's algorithm

Highest Common Factor of 752,480,699 is 1

Step 1: Since 752 > 480, we apply the division lemma to 752 and 480, to get

752 = 480 x 1 + 272

Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 272 and 480, to get

480 = 272 x 1 + 208

Step 3: We consider the new divisor 272 and the new remainder 208, and apply the division lemma to get

272 = 208 x 1 + 64

We consider the new divisor 208 and the new remainder 64,and apply the division lemma to get

208 = 64 x 3 + 16

We consider the new divisor 64 and the new remainder 16,and apply the division lemma to get

64 = 16 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 752 and 480 is 16

Notice that 16 = HCF(64,16) = HCF(208,64) = HCF(272,208) = HCF(480,272) = HCF(752,480) .

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

Step 1: Since 699 > 16, we apply the division lemma to 699 and 16, to get

699 = 16 x 43 + 11

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 11 and 16, to get

16 = 11 x 1 + 5

Step 3: We consider the new divisor 11 and the new remainder 5, and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 699 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(699,16) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 752, 480, 699 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 752, 480, 699?

Answer: HCF of 752, 480, 699 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 752, 480, 699 using Euclid's Algorithm?

Answer: For arbitrary numbers 752, 480, 699 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.