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What's So Special About This Number?

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Facts about 6

6 is even

The factors of 6 are 1, 2, 3 and 6 and the proper factors of 6 are 1, 2, and 3.

6 is the smallest perfect number becauseits proper factors add up to itself. 1 + 2 + 3 = 6

6 is the only number (except 1) such that the sum of all the primes less than 6 equals the sum of all the composite numbers up to and including 6 2+3+5=4+6

6 is the only number that is both the sum and the product of the same three distinct positive integers 1x2x3=6=1+2+3

6 is a triangular number

6 is a curious number because the units digit of 6x6=36 is 6.

6 is a pronic number because it is a product of two consecutive numbers 6=2x3

Facts about 7

7 is a prime number because it has exactly two factors, 1 and 7.

7 is the only prime which is one less than a perfect cube : 7 = 2x2x2 –1

There are 7 primes less than 77 that have at least one digit being 7: 7, 17, 37, 47, 67, 71, 73

There are 7 letters in TUESDAY, which is the only day of the week whose name contains a prime number of letters.

The sum of the 7 primes beginning with 7 is 7 times the 7th prime. 7+11+13+17+19+23+29=119=7x17

Using A = 1, B = 2, ..., Z = 26, the sum of all the letter values in the word names of the numbers from 1 to 7 is a prime (367). If 0 is included, the sum is yet another prime (431).

Double 7! to get the exact number of minutes in a week (7 days).

7 is the smallest integer that is not the difference of two primes

7 is the number of visible colors formed by light across a prism.

There are 7 different notes in a standard major scale in music as well as in a standard minor scale.

7 is the sum of the numbers on opposite sides of a standard die.

If asked to quickly pick a number between 12 and 5, most people will choose 7.

7 is the first prime happy number. Replace a number by the sum of the squares of its digits, and repeat the process until the number equals 1, or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are called happy numbers. There are exactly 7 prime happy numbers less than 100. Can you find all 7?

Facts about 8

8 is composite because it has more than 2 factors.

8 is deficient because the sum of its proper factors is less than 8: 1+2+4=7

8 is the largest cube (2x2x2) in the Fibonacci sequence.

8 is the smallest sum of two factorials of distinct primes: 2! + 3!

8 is the only cube that is 1 less than a square (3x3 – 1).

8 is the smallest number (except 1) which is equal to the sum of the digits of its cube: 8x8x8=512 5+1+2=8

Square any odd number and then divide by 8; the remainder is always 1.

8 + 8 + 8 + 88 + 888 = 1000

A base-8 (octal) numeral system was devised by the Yuki of Northern California, who used the spaces between the fingers to count.