Question

find the least prime factor of the number 2016 - 3 / 2016 3​

Answer 1

Answer:

Step-by-step explanation:

Finding the least prime factor is typically an iterative process seeking the smallest prime number that evenly divides a given number. However, quick rules can be applied to some numbers as follows:

1. The least prime factor for all even numbers is 2

2. A prime number is its own least prime factor

3. Any odd number whose sum of all digits are evenly divided by 3 will also be evenly divided by 3 and therefore 3 is the least prime factor (example: try 3591 with the sum of digits = 18)

4. A number that ends in a 5 that is not evenly divisible by 3 will be evenly divisible by 5 as the least common factor (example: try 65 but watch out for 45 and 75)

5. For numbers evenly divisible by 7 after establishing non even divisibility by 3

a. Take the last digit

b. Double it

c. Subtract the doubled value from the remaining number

d. Check to see if the part c value is 0 or divisible by 7

(example: try 161) 2*1 = 2 16-2 = 14 and is evenly divisible by 7 which is the least prime factor for 161

There are a number of tests for divisibility by other prime numbers greater than 7 but these five quick rules can be applied with relative ease.

Answer 2

Answer:

The least prime factor of the number is 2

Step-by-step explanation:

Given: 2016-3

Factors of 2013:

By prime factorization of 2013 we follow 5 simple steps:

1. We write number 2013 above a 2-column table

2. We divide 2013 by the smallest possible prime factor

3. We write down on the left side of the table the prime factor and next number to factorize on the ride side

4. We continue to factor in this fashion (we deal with odd numbers by trying small prime factors)

5. We continue until we reach 1 on the ride side of the table

2013

prime factors number to factorize

3 671

11 61

61 1

Factors of 2013 = 1×3×11×61= 1×3×11×61

Given: $2016*3$

Factors of 6048:

By prime factorization of 6048 we follow 5 simple steps:

1. We write number 6048 above a 2-column table

2. We divide 6048 by the smallest possible prime factor

3. We write down on the left side of the table the prime factor and next number to factorize on the ride side

4. We continue to factor in this fashion (we deal with odd numbers by trying small prime factors)

5. We continue until we reach 1 on the ride side of the table

6048

prime factors number to factorize

$2 \ 3024\\2 \ 1512\\2 \ 756\\2 \ 378\\2 \ 189\\3 \ 63\\3 \ 21\\3 \ 7\\7 \ 1$

Factors of 6048

$= 1*2*2*2*2*2*3*3*3*7\\= 1*2^5*3^3*7^1$

3 is the least prime factor of number a and 2 is the least prime factor of number b.

Therefore,

a should be greater than or equal to 3

b should be greater than or equal to 2.

Now, consider the case

a = 3

b = 2

Then,

a + b = 3 + 2

Therefore a + b = 5

We know that 2 is the least prime factor of a + b.

Let us consider the case

$a = 3^2= 9$

$b =2^2 = 4$

It is clear that a + b = 13 (odd number).

Similarly, for the value of n, an + bn is divisible by 2.

∴ The least prime factor of a + b is 2.

Reference Link

• https://brainly.in/question/1228270
• https://brainly.in/question/17863028