96 (number) facts for kids

96 is a natural number that comes right after 95 and just before 97. It's a number with some interesting features! For example, 96 is considered a strobogrammatic number. This means that if you rotate its digits 180 degrees (imagine turning it upside down), the digits 6 and 9 swap places, forming the number 69.

Exploring the Number 96

What Makes 96 Special in Math?

The number 96 has many unique properties that mathematicians find interesting. Let's explore some of them!

96: A Number with Many Divisors

A divisor is a number that divides another number exactly, without leaving a remainder. The number 96 has 12 divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. Because 96 has more divisors than any smaller number, it is called a largely composite number. This means it's made up of many smaller factors.

96 shown as the difference of two squares.

Strobogrammatic and Palindromic Fun

As we mentioned, 96 is a strobogrammatic number. This means its digits (9 and 6) are a special pair. When you rotate them 180 degrees, the 9 becomes a 6, and the 6 becomes a 9. So, 96 rotated looks like 69!

96 is also a palindromic number in several different bases. A palindromic number reads the same forwards and backwards. For example, in base 11, 96 is written as 88. In base 15, it's 66. And in base 23, it's 44. These numbers read the same both ways!

Octagonal and Abundant Numbers

96 is an octagonal number. Imagine arranging dots to form a shape. Octagonal numbers are numbers that can form a regular octagon.

It's also an abundant number. To understand this, you need to find all its proper divisors (divisors excluding the number itself). For 96, these are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48. If you add these up (1+2+3+4+6+8+12+16+24+32+48), the sum is 156. Since 156 is greater than 96, 96 is an abundant number!

Semiperfect and Refactorable

96 is a semiperfect number. This means you can find some of its proper divisors that add up to 96 itself. For example, 48 + 32 + 16 = 96.

It is also a refactorable number. This means that the number of its divisors (which is 12) actually divides the number itself (96 ÷ 12 = 8). How neat is that?

Granville Number

96 is known as the fourth Granville number. These are special numbers related to their divisors. The previous Granville number was 24, and the next one is 126.

Difference of Squares

Did you know that 96 can be written as the difference between two square numbers in many ways? A square number is a number multiplied by itself (like 4x4=16). Here are some examples for 96:

• 10² - 2² = 100 - 4 = 96
• 11² - 5² = 121 - 25 = 96
• 14² - 10² = 196 - 100 = 96
• 25² - 23² = 625 - 529 = 96

It's the smallest natural number that can be shown this way in more than three different ways!

Divisible by Prime Counts

A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Below 96, there are 24 prime numbers (like 2, 3, 5, 7, and so on). Interestingly, 96 is perfectly divisible by this count: 96 ÷ 24 = 4.

See also

In Spanish: Noventa y seis para niños