Highest Common Factor of 460, 740, 830 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 460, 740, 830 i.e. 10 the largest integer that leaves a remainder zero for all numbers.

HCF of 460, 740, 830 is 10 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 460, 740, 830 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 460, 740, 830 is 10.

HCF(460, 740, 830) = 10

HCF of 460, 740, 830 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 460, 740, 830 is 10.

Highest Common Factor of 460,740,830 using Euclid's algorithm

Highest Common Factor of 460,740,830 is 10

Step 1: Since 740 > 460, we apply the division lemma to 740 and 460, to get

740 = 460 x 1 + 280

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 280 and 460, to get

460 = 280 x 1 + 180

Step 3: We consider the new divisor 280 and the new remainder 180, and apply the division lemma to get

280 = 180 x 1 + 100

We consider the new divisor 180 and the new remainder 100,and apply the division lemma to get

180 = 100 x 1 + 80

We consider the new divisor 100 and the new remainder 80,and apply the division lemma to get

100 = 80 x 1 + 20

We consider the new divisor 80 and the new remainder 20,and apply the division lemma to get

80 = 20 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 460 and 740 is 20

Notice that 20 = HCF(80,20) = HCF(100,80) = HCF(180,100) = HCF(280,180) = HCF(460,280) = HCF(740,460) .

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

Step 1: Since 830 > 20, we apply the division lemma to 830 and 20, to get

830 = 20 x 41 + 10

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 10 and 20, to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 20 and 830 is 10

Notice that 10 = HCF(20,10) = HCF(830,20) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 460, 740, 830 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 460, 740, 830?

Answer: HCF of 460, 740, 830 is 10 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 460, 740, 830 using Euclid's Algorithm?

Answer: For arbitrary numbers 460, 740, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.