Highest Common Factor of 402, 712, 521, 735 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 402, 712, 521, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 402, 712, 521, 735 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 402, 712, 521, 735 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 402, 712, 521, 735 is 1.

HCF(402, 712, 521, 735) = 1

HCF of 402, 712, 521, 735 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 402, 712, 521, 735 is 1.

Highest Common Factor of 402,712,521,735 using Euclid's algorithm

Highest Common Factor of 402,712,521,735 is 1

Step 1: Since 712 > 402, we apply the division lemma to 712 and 402, to get

712 = 402 x 1 + 310

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 310 and 402, to get

402 = 310 x 1 + 92

Step 3: We consider the new divisor 310 and the new remainder 92, and apply the division lemma to get

310 = 92 x 3 + 34

We consider the new divisor 92 and the new remainder 34,and apply the division lemma to get

92 = 34 x 2 + 24

We consider the new divisor 34 and the new remainder 24,and apply the division lemma to get

34 = 24 x 1 + 10

We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get

24 = 10 x 2 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 402 and 712 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(34,24) = HCF(92,34) = HCF(310,92) = HCF(402,310) = HCF(712,402) .

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

Step 1: Since 521 > 2, we apply the division lemma to 521 and 2, to get

521 = 2 x 260 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 521 is 1

Notice that 1 = HCF(2,1) = HCF(521,2) .

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

Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get

735 = 1 x 735 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1

Notice that 1 = HCF(735,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 402, 712, 521, 735 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 402, 712, 521, 735?

Answer: HCF of 402, 712, 521, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 402, 712, 521, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 402, 712, 521, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.