Highest Common Factor of 603, 746, 961 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 603, 746, 961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 603, 746, 961 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 603, 746, 961 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 603, 746, 961 is 1.

HCF(603, 746, 961) = 1

HCF of 603, 746, 961 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 603, 746, 961 is 1.

Highest Common Factor of 603,746,961 using Euclid's algorithm

Highest Common Factor of 603,746,961 is 1

Step 1: Since 746 > 603, we apply the division lemma to 746 and 603, to get

746 = 603 x 1 + 143

Step 2: Since the reminder 603 ≠ 0, we apply division lemma to 143 and 603, to get

603 = 143 x 4 + 31

Step 3: We consider the new divisor 143 and the new remainder 31, and apply the division lemma to get

143 = 31 x 4 + 19

We consider the new divisor 31 and the new remainder 19,and apply the division lemma to get

31 = 19 x 1 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 603 and 746 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(31,19) = HCF(143,31) = HCF(603,143) = HCF(746,603) .

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

Step 1: Since 961 > 1, we apply the division lemma to 961 and 1, to get

961 = 1 x 961 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 961 is 1

Notice that 1 = HCF(961,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 603, 746, 961 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 603, 746, 961?

Answer: HCF of 603, 746, 961 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 603, 746, 961 using Euclid's Algorithm?

Answer: For arbitrary numbers 603, 746, 961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.