The number system includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures as well as words accordingly. For example, the numbers like 40 and 65 expressed in the form of figures can also be written as forty and sixty-five. A Number system or numeral system is defined as an elementary system to express numbers and figures. It is a unique way of representing numbers in arithmetic and algebraic structure.
What are Numbers?
Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system. Numbers generally are also known as numerals are the mathematical values used for counting, measurements, labeling, and measuring fundamental quantities.
Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2, 4, 7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
Types of Numbers
There are different types of numbers categorized into sets by the number system. Numbers are defined based on their different characteristics. The types are described below,
- Natural numbers: Natural numbers are the positive numbers that count from 1 to infinity. The set of natural numbers is represented by N. It is the number we generally use for counting. The set of natural numbers can be represented as N = 1, 2, 3, 4, 5, 6, 7…
- Whole numbers: Whole numbers are positive numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by W. The set can be represented as W = 0, 1, 2, 3, 4, 5…
- Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by Z. The set of integers can be represented as Z=…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,…
- Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can be expressed as 2.5, 0.567, etc.
- Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by R.
- Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a + bi where “a” and “b” are real numbers. It is denoted by C.
- Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by Q.
- Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by P.
What two numbers multiply to 500?
Numbers multiplying to form a bigger number are known to be the factors of that number. Therefore, first, let’s understand the factors in order to understand the answer to the above problem statement,
Factors
A number that divides the given number is defined as the factor of number and a factor is nothing but a divisor of the given number. To find the factor, we can use both the multiplication as well as the division method. A number that divides another number evenly which gives us no remainder is a factor of a number. It can be algebraic expressions as well and dividing another expression evenly.
For example, let’s find the factors of 10. Hence by factorization, it can be written 1 × 10 and 2 × 5. The product of two negative numbers is a positive number only. Hence, the factors of 10 are 1, -1, 2, -2, 5, -5, 10, and -10, but when it comes to finding the factor of a number, we only considered positive numbers, which too also include only a whole number, not a fractional number, these are the numbers that can be used for multiplication to get 10, numbers are (1 × 10 ), (2 × 5).
Solution:
To find the numbers , use prime factorisation method to find out the factors of 500.
So here prime factorisation of 500 are 22 × 53 = 2 × 2 × 5 × 5 × 5
Through prime factorisation ,we can use combinations of numbers which multiply to get 500 are,
(2 × 2) × (5 × 5 × 5) = 4 × 125
(2 × 2 × 5) × (5 × 5) = 20 × 25
(2 × 2 × 5 × 5) × (5) = 100 × 5
(2) × (2 × 5 × 5 × 5) = 2 × 250
(2 × 5) × (2 × 5 × 5) = 10 × 50
(1 × 500) is also a factor of 500
So here 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500 are the factors of 500
Hence, these are the numbers we can use for the multiplication to get 500.
Similar Problems
Question 1: What numbers can multiply to get 100?
Solution:
Prime factorisation of 100 are 2 × 2 × 5 × 5
Hence, (2 × 2 × 5) × 5 = 20 × 5 = 100
(2) × (2 × 5 × 5) = 2 × 50 = 100
(2 × 5) × (2 × 5) = 10 × 10 = 100
(2 × 2) × (5 × 5) = 4 × 25 = 100
Hence the numbers we can multiply to get 100 are 1, 2, 4, 5, 10, 20, 25, 100.
Question 2: what numbers can multiply to get 600?
Solution:
Prime factorization of 600 are 2 × 2 × 2 × 3 × 5 × 5
Hence, (2 × 2 × 2 × 3) × (5 × 5) = 24 × 25 = 600
(2 × 2 × 2) × (3 × 5 × 5) = 8 × 75 = 600
(2 × 2) × (2 × 3 × 5 × 5) = 4 × 150 = 600
(2) × (2 × 2 × 3 × 5 × 5) = 2 × 300 = 600
(3) × (2 × 2 × 2 × 5 × 5) = 3 × 200 = 600
(3 × 2) × (2 × 2 × 5 × 5) = 6 × 100 = 600
(3 × 2 × 2) × (2 × 5 × 5) = 12 × 50 = 600
(3 × 2 × 2 × 2 × 5) × (5) = 120 × 5 = 600
(3 × 5) × (2 × 2 × 2 × 5) = 15 × 40 = 600
(2 × 5) × (2 × 2 × 3 × 5) = 10 × 60 = 600
(1) × (2 × 2 × 2 × 3 × 5 × 5) = 1 × 600 = 600
(2 × 2 × 5) × (2 × 3 × 5) = 20 × 30 = 600
(2 × 2 × 5 × 5) × (2 × 3) = 100 × 6 = 600
Hence the factors of 500 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.
These are the numbers that can be used for multiplication to get 600.