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Whole Numbers

Terms

Introduction and Summary

Place Value

Base Ten  -  System in which ten digits are used in combination to represent all numbers. The system also uses the concept of place value, wherein each place has a value greater by a factor of 10 than the value of the place to its right. The digit in each place represents a number that is equal to that numeral times 10 raised to a certain power. For example, the "5" in "6,589" represents 5×102 .
Composite  -  A whole number that has at least one factor besides 1 and itself; e.g. any whole number greater than 1 and not prime.
Divisible  -  A number is divisible by another number if it can be divided equally by that number; that is, if it yields a whole number when divided by that number. 12 is divisible by 4 because 12/4 = 3 , and 3 is a whole number. 12 is not divisible by 10, because 12/10 = 1.2 , and 1.2 is not a whole number.
Decimal System  -  Our system of numeration. The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, used in combination, represent all numbers.
Factor  -  A number by which another number is divisible. 1, 2, 3, and 6 are all factors of 6, because 6/1, 6/2, 6/3, and 6/6 are all whole numbers.
Greatest Common Factor  -  The greatest (largest) number that divides two or more given numbers.
Least Common Multiple  -  The smallest number that is divisible by two or more given numbers.
Multiple  -  A number that can be obtained by multiplying a given number by a whole number. 6, 9, and 12 are all multiples of 3, because 3×2 = 6 , 3×3 = 9 , and 3×4 = 12 . If a is a factor of b , then b is a multiple of a .
Place Value  -  The value of a digit, based on where it appears in a numeral. The value of each position in a numeral is ten times the value of the position to its right. The numeral 30,482 has a "2" in the ones place, an "8" in the tens place, a "4" in the hundreds place, a "0" in the thousands place, and a "3" in the ten thousands place. The number 1.567 has a "1" in the ones place, a "5" in the tenths place, a "6" in the hundredths place, and a "7" in the thousandths place.
Prime  -  A positive whole number divisible only by 1 and itself. Following are the first fifteen prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ... (Note: 1 is not considered prime).
Prime Factorization  -  A number written as the product of its prime factors.
Relatively Prime  -  Two numbers that have no common prime factors and thus have a greatest common factor of 1. For example, 64 and 295 are relatively prime, since they share no prime factors.
Whole Number  -  The set of numbers which includes zero and all the counting numbers--no fractions or decimals. 0, 1, 2, 3, 4, 5, 6, ...

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