What is the prime factorization of 1400?

2 Answers
Feb 11, 2018

2xx2xx2xx5xx5xx7

Explanation:

To find the prime factorization of 1400, we need to break it down into prime factors.

Lets use these steps I found in here: https://www.wikihow.com/Find-Prime-Factorization Follow along!

Step 1: Understand factorization. Hopefully you do, but just in case I'll explain.

  • Factorization: the process of breaking a larger number into smaller numbers (algebraic definition)

Step 2: Know prime numbers. They are basically numbers that can only be factored by 1 and itself. e.g. 5 (5xx1), 47 (47xx1)

Step 3: Start with the number, which is 1400. It is always helpful to rewrite the problem, for it is easy to make mistakes if you don't.

Step 4: Start by factoring the number into any two factors.

  • 1400: 200xx7

Step 5: If the factorization continues, start a factorization tree, so it is less vulnerable to mistakes.
- 1400
-tttt^
- 200 7

Step 6: Continue factorization.

  • 1400
  • tttt^
  • 200 7
  • ttt^
  • 100 2
  • ttt^
  • 50 2
  • ttt^
  • 25 2
  • t^
  • 5 5

Step 7: Note any Prime numbers.

  • 1400
  • tttt^
  • 200 color(red)7
  • ttt^
  • 100 color(red)2
  • ttt^
  • 50 color(red)2
  • ttt^
  • 25 color(red)2
  • t^
  • color(red)5 color(red)5

Step 8: Finish factorization. I already did this in the 6th step, so...

Step 9: Finish by writing the line of prime factors neatly in increasing order.

  • color(blue)(1400: 2xx2xx2xx5xx5xx7)
Feb 13, 2018

The prime factors of 1400 " are " 2,5,7

1400 = 2xx2xx2xx5xx5xx7

Explanation:

The intention of the question is not absolutely clear....

Is it asking which of the factors of 1400 are prime numbers?

Or

Is it asking for 1400 to be written as the product of its prime factors.

It will help to write 1400 as the product of its prime factors anyway..

Divide 1400 by prime numbers which are factors until you get 1

2 |ul(color(white)(.)1400)
2 |ul(" "700)
2 |ul(" "350)
5 |ul(" "175)
5 |ul(" "35)
7 |ul(" "7)
color(white)(..ww...)1

The prime factors of 1400 " are " 2,5,7

As the product of its prime factors:

1400 = 2xx2xx2xx5xx5xx7