Basics and Number Theory - Kuta

Place value

100 one hundred ten tens 1,000 one thousand ten hundreds 10,000 ten thousand ten thousands 100,000 one hundred thousand one hundred thousands 1,000,000 one million one thousand thousands Name American-French English-German million 1,000,000 1,000,000 billion 1,000,000,000 (a thousand millions) 1,000,000,000,000 (a million millions) trillion 1 with 12 zeros 1 with 18 zeros quadrillion1 with 15 zeros 1 with 24 zeros quintillion 1 with 18 zeros 1 with 30 zeros sextillion 1 with 21 zeros 1 with 36 zeros septillion 1 with 24 zeros 1 with 42 zeros octillion 1 with 27 zeros 1 with 48 zeros googol 1 with 100 zeros googolplex 1 with a googol of zeros

Least common multiple (LCM)

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, .... The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. The LCM of 3 and 4 is 12

Composite number

A composite number is any number that has more than two factors. Here's a list of composite numbers up to 20. You can see that they can all be factored further. For example, 4 equals 2 times 2, 6 equals 3 times 2, 8 equals 4 times 2, and so forth. By the way, zero and one are considered neither prime nor composite numbers-they're in a class by themselves! COMPOSITE NUMBERS up to 20 4,6,8,9,10,12,14,15,16,18,20

Factor

A factor is simply a number that is multiplied to get a product. Factoring a number means taking the number apart to find its factors--it's like multiplying in reverse. Here are lists of all the factors of 16, 20, and 45. 16 --> 1, 2, 4, 8, 16 20 --> 1, 2, 4, 5, 10, 20 45 --> 1, 3, 5, 9, 15, 45

PRIME NUMBER

A prime number has only two factors, one and itself, so it cannot be divided evenly by any other numbers. Here's a list of prime numbers up to 100. You can see that none of these numbers can be factored any further. PRIME NUMBERS to 100 2,3,5,7,11,13,17,19,23,29,31,37,41,43, 47,53,59,61,67,71,73,79,83,89,97

Fractions

Digits to the right of the decimal point represent the fractional part of the decimal number. Each place value has a value that is one tenth the value to the immediate left of it. Number Name Fraction .1 tenth 1/10 .01 hundredth 1/100 .001 thousandth 1/1000 .0001 ten thousandth 1/10000 .00001 hundred thousandth 1/100000

Factors

Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite).

Roman Numerals

Roman Numerals I =1 (I with a bar is not used) V=5 _ V=5,000 X=10 _ X=10,000 L=50 _ L=50,000 C=100 _ C = 100 000 D=500 _ D=500,000 M=1,000 _ M=1,000,000

Greatest common factor (GCF)

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers 1.List the prime factors of each number. 2.Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Prime factorization.

You can write any composite number as a product of prime factors. This is called prime factorization. Ex:168 ÷ 2 = 84 84 ÷ 2 = 42 42 ÷ 2 = 21 21 ÷ 3 = 7 Prime number prime factors = 2 × 2 × 2 × 3 × 7