Write the following as the product of its primes:?

Question

a) 144
b) 128
c) 425
can you please let me know how do the breakdown

Answer 1

just divide down till you get ALL prime numbers
144= 2* 72
144 =2*2*36
144= 2*2*2*18
144 = 2*2*2*2*9
144 = 2*2*2*2*3*3
144= 2^4*3^2
2 to the fourth times 3 squared

b)128
128 = 2*64
128 = 2*2*32
128 = 2*2*2*16
128 = 2*2*2*4*4
128 = 2*2*2*2*2*2*2
128 = 2^7
2 to the seventh

c)425
425 = 25 *17
425 = 5*5*17
5^2*17
five squared times 17

Answer 2

Well... What you do is find two factors of 144... [meaning what two numbers when multiplied together form 144?]. I'll use 12 & 12, but you can of course use many other numbers:

144
12 12


Now... You find factors of 12, I'll use, 4 & 3, because they are easy. :)

144
12 12
4 3 4 3

3 is a prime number, thus it stays the same, but 4 can be broken into 2x2. Therefore:

144
12 12
4 3 4 3
2 2 3 2 2 3

Therefore... 144 is equal to 2x2x3x2x2x3. <-- They are all prime numbers thus 2x2x3x2x2x3 is the product of primes for 144.

You do the same thing for the others... So:

128
8 16
2 4 4 4
2 2 2 2 2 2 2

= 2x2x2x2x2x2x2 = 2^7



c)

425
25 17
5 5 17

=5x5x17




Hope that helped... Any questions ask away. :)

And also, there is mainly imaginary multiplication signs in between the numbers on the tree. :)

Answer 3

144 is an even number, divide by 2 until an odd number appears:
144/2 = 72
72/2 = 36
36/2 = 18
18/2 = 9
9 is odd, but not prime; however 3 is, so the two primes are "2" and "3"

128 works the same way. The primes are "2" and "1"

425 is odd, but the "5" means it is divisible by "5" :

425/5 = 85
85/5 = 17

17 is prime, so the two primes are "5" and "17"

BTW: "1" can be included in any of the answers since it is prime and all things are divisible by 1.

Answer 4

To break down a number to form a product of its prime, you would need to do a prime factorisation.
For example, 144.

Divide 144 by the smallest divisible prime number 2.
You would get 72.
Again, divide 72 by the smallest divisible prime number 2.
You would get 36.
Again, divide 36 by the smallest divisible prime number 2.
You would get 18.
Again, divide 18 by the smallest divisible prime number 2.
You would get 9.
Again, divide 9 by the next smallest divisible prime number 3.
You would get 3.
Lastly, divide 9 by the smallest divisible prime number 3.
You would get 1.

Count the number of twos and threes you have divided.
Expressing 144 as a product of its primes,
144 = 2^4 x 3^2

Another example is 128.

Divide 128 by the smallest divisible prime number 2.
You would get 64.
Again, divide 64 by the smallest divisible prime number 2.
You would get 32.
Again, divide 32 by the smallest divisible prime number 2.
You would get 16.
Again, divide 16 by the smallest divisible prime number 2.
You would get 8.
Again, divide 8 by the smallest divisible prime number 2.
You would get 4.
Again, divide 4 by the smallest divisible prime number 2.
You would get 2.
Lastly, divide 2 by the smallest divisible prime number 2.
You would get 1.

Count the number of twos you have divided against.
Expressing 128 as a product of its primes,
128 = 2^7

You can try out the last one yourself.

Answer 5

144=12*12=3.3. 2^4
128= 2^7
425=5^2. 17

Answer 6

a) 144=2^4x3^2
b)128=2^7
c)425=5^2x17.

Answer 7

a) 2 * 2 * 2 * 2 * 3 * 3 or (2 *3)^2 * 2^2
b) 2^7
c) 5 * 5 * 17 or 5^2 * 17