Factors of 400

Did you know that on average, children smile 400 times a day? 400 is a composite number and is a perfect square. In this short lesson, we are going to learn about the factors of 400 and the different ways to find them. We will explore more about the prime factors of 400, factors of 60, factors of 400 in pairs, and the prime factorization of 400 using interactive examples. 

• Factors of 400:1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200
• Prime Factorization of 400: 2 × 2 × 2 × 2  × 5 × 5 

The factor of a number is a number that divides it completely, i.e., without leaving any remainder. The number 400 is an even composite number. Factors of 400 are all the integers that 400 can be divided into. We can also say that factors of 400 are the numbers which, when multiplied together, result in 400.

•  400 = 1 × 400
•  400 = 2 × 200
•  400 = 4 × 100
•  400 = 5 × 80
•  400 = 8 × 50
•  400 =10 × 40
•  400 = 16 × 25
•  400 = 20 × 20 

Explore factors using illustrations and interactive examples.

• Factors of 360:  The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
• Factors of 225: The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
• Factors of 300: The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
• Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
• Factors of 45: The factors of 45 are 1, 5, 9, and 45.

• Let's begin calculating the factors of 400, starting with the whole number 1. Keep dividing 400 by each number with the help of the divisibility rules too.
• 400 ÷ 1 = 400 and the remainder is 0.
• 400 ÷ 2 = 200 and the remainder is 0.
• Proceeding in a similar manner we get all the factors of 400 as 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400. 

Prime factorization means expressing a composite number as the product of its prime factors.

• To get the prime factorization of 400, we divide it by its smallest prime factor, which is 2. 400÷ 2 = 200
• Now, 200 is divided by its smallest prime factor and the quotient is obtained. 200÷ 2 = 100
• This process goes on till we get the quotient as 1. 
• The prime factorization of 400 is shown below:

• Let us express 400 in terms of the product of its prime factors with the help of the factor tree obtained. 400= 2 × 2 × 2 × 2 × 5 × 5 = 2⁴ × 5^2.. Now that we have done the prime factorization of our number, we can multiply them and get the other possible composite factors.

• Can a number greater than 400 be its factor?
• What is the value of 2⁵ ?

The negative factor pairs of 400 are (-1,-400), (-2,-200), (-4,-100), (-5, -80), (-8, -50), (-10,-40), (-16,-25), and (-20,-20).

• As 400 is an even number, it will have 2 as its factor.
• Only composite numbers can have more than two factors.
• Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.