Highest Common Factor of 960, 620, 448 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 960, 620, 448 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 960, 620, 448 is 4 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 960, 620, 448 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 960, 620, 448 is 4.

HCF(960, 620, 448) = 4

HCF of 960, 620, 448 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 960, 620, 448 is 4.

Highest Common Factor of 960,620,448 using Euclid's algorithm

Highest Common Factor of 960,620,448 is 4

Step 1: Since 960 > 620, we apply the division lemma to 960 and 620, to get

960 = 620 x 1 + 340

Step 2: Since the reminder 620 ≠ 0, we apply division lemma to 340 and 620, to get

620 = 340 x 1 + 280

Step 3: We consider the new divisor 340 and the new remainder 280, and apply the division lemma to get

340 = 280 x 1 + 60

We consider the new divisor 280 and the new remainder 60,and apply the division lemma to get

280 = 60 x 4 + 40

We consider the new divisor 60 and the new remainder 40,and apply the division lemma to get

60 = 40 x 1 + 20

We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get

40 = 20 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 960 and 620 is 20

Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(280,60) = HCF(340,280) = HCF(620,340) = HCF(960,620) .

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

Step 1: Since 448 > 20, we apply the division lemma to 448 and 20, to get

448 = 20 x 22 + 8

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 8 and 20, to get

20 = 8 x 2 + 4

Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 448 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(448,20) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 960, 620, 448 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 960, 620, 448?

Answer: HCF of 960, 620, 448 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 960, 620, 448 using Euclid's Algorithm?

Answer: For arbitrary numbers 960, 620, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.