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What Are The Factors Of 60

What are the factors of 60? Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The number 60 has 12 factors(we also counted the integer itself and 1 as elements). All numbers are divisible by 1 and itself. The biggest factor of 60 is 30. The smallest factor of 60 is 2.

What Are The Factor Pairs Of 60

All whole numbers in a factor pair have to be factors of the given number(in this case 60). When multiplying factor pairs of 60 together the result has to be equal to 60. List for factor pairs of 60:

1×60 is a factor pair of 60 because 1×60=60
2×30 is a factor pair of 60 because 2×30=60
3×20 is a factor pair of 60 because 3×20=60
4×15 is a factor pair of 60 because 4×15=60
5×12 is a factor pair of 60 because 5×12=60
6×10 is a factor pair of 60 because 6×10=60


We found 6 factors of 60 in pairs.

How To Check If All Factors Of 60 Are Correct Answers

All the factors of 60 have to divide with this number without leaving a remainder to be correct. If division leaves a remainder then this means that the integer is not a factor. Now let us check all factors with this principle:

60/1=60 has a remainder of 0 which makes it divisible by the factor 1
60/2=30 has a remainder of 0 which makes it divisible by the factor 2
60/3=20 has a remainder of 0 which makes it divisible by the factor 3
60/4=15 has a remainder of 0 which makes it divisible by the factor 4
60/5=12 has a remainder of 0 which makes it divisible by the factor 5
60/6=10 has a remainder of 0 which makes it divisible by the factor 6

After having checked all 12 components we can now safely say that they are correct answers.

General Mathematical Properties Of Number 60

60 is a composite number. 60 is a composite number, because it has more divisors than 1 and itself. This is an even number. 60 is an even number, because it can be divided by 2 without leaving a comma spot. This also means that 60 is not an odd number. When we simplify Sin 60 degrees we get the value of sin(60)=-0.30481062110222. Simplify Cos 60 degrees. The value of cos(60)=-0.95241298041516. Simplify Tan 60 degrees. Value of tan(60)=0.32004038937956. When converting 60 in binary you get 111100. Converting decimal 60 in hexadecimal is 3c. The square root of 60=7.7459666924148. The cube root of 60=3.9148676411689. Square root of √60 simplified is 2√15. All radicals are now simplified and in their simplest form. Cube root of ∛60 simplified is 60. The simplified radicand no longer has any more cubed factors.

All Factors Of Smaller Numbers Than 60 Solved

Learn how to calculate components of smaller integers like:

All Factors Of Bigger Numbers Than 60 Solved

Learn how to calculate components of bigger numbers such as:

Single Digit Properties For 60 Explained

  • Integer 6 properties: 6 is even and a composite, with the following divisors:1, 2, 3, 6. Also called perfect number since the sum of the divisors(excluding itself) is 6. The first perfect figure, the next ones are 28 and 496. Six is highly a composed, semiprimo, congruent, scarcely total, Ulam, Wedderburn-Etherington, multi-perfect, integer-free number. Complete Harshad, which is a quantity of Harshad in any expressed base. The factorial of 3 and a semi-perfect digit. The third triangular and the first hexagonal value. All perfect even amounts are triangular and hexagonal. Six is the smallest amount different from 1 whose square (36) is triangular(the next in the line that enjoys this property is 35). Strictly a non-palindrome. A numeral is divisible by 6 if and only if it is divisible by both 2 and 3. Part of the Pythagorean triple (6, 8, 10). Being the product of the first two primes (6=2×3), it is a primitive. In the positional numbering system based on 5 it is a repeated number. An oblong, of the form n(n+1).
  • Integer 0 properties: 0 is the only real figure that is neither positive nor negative. Sometimes it is included in natural numbers where it can be considered the only natural in addition to the one to be neither first nor composed, as well as the minimum of natural numbers(that is, no natural digit precedes the 0). In an oriented line (which makes a point on the straight line correspond to each real number, preserving also the relation of order), the 0 coincides conventionally with the origin. Since it can be written in the form 2k, with con k integer, 0 is called even. It is both a figure and a numeral. In set theory, the zero is the cardinality of the empty set. In fact, in certain axiomatic mathematical developments derived from set theories, zero is defined as the empty set. In geometry, the size of a point is 0. Zero is the identity element of an additive group or additive identity in a ring.

Finding All Factors Of A Number

How did we find all the 12 components of 60? We simply used one of the divisibility or multiplication methods explained below.

How to Factor A Number With Divisibility?


We want to find all of the whole numbers that your figure is divisible by. Start dividing your number one after another with all numbers that are smaller than itself(for 60 you would have to make half the amount of divisions). All numbers that leave no remainder after division are components of the integer!

This is a simple yet also a very time consuming method. Not practical to use when dealing with large numbers.

How To Factor A Integer With Multiplication?


To find all the components of a given figure you start by multiplying with 1* (Example 1*60=60) then with 2*x, 3*x, 4*x and so on. A pair of numbers that when multiplied together equals 60 can be called the factors of 60(a factor pair of this integer).

This is also called the rainbow method, because you can write the smaller factors on the left and the bigger ones on the right side. Example:

List with all the components of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Gradually these factors will start to close in on each other. Once the gap between big and small elements is closed and they start to meet, then you know that all elements are found.

Tips For Finding Factors Easily

Simplify math by using these six tips for finding factors the easy way.

Tip 1: If the last digit of a bigger number is 0, 2, 4, 6 or 8 then this means that the whole number is an even number. If it is an even amount it is divisible by 2(making 2 a factor).

Tip 2: By multiplying the prime factors of a given number, we can find new factors.

Tip 3: If the sum of digits of a number is divisible by 3 then the figure is also divisible by 3(making 3 a factor). Example: the digits of 24 are 2 and 4 so 2+4=6 and 6 is divisible by 3, meaning that 24 is divisible by 3. The same logic also works for 9.

Tip 4: If the last two digits of a number are 00 then this integer is divisible by 4(knowing multiples of 4 comes in handy when using this). Making 4 a component.

Tip 5: If the last digit of a figure is 0 or 5 then 5 is a component of this number, because it is divisible.

Tip 6: All numbers that are divisible by both 2 and 3 are also divisible by 6. By using our third and sixth tip together you can now easily check if 6 is a factor in a big number.

What Are Factors Of A Number?

Whole numbers that are divisible without leaving any fractional part or remainder are called factors of a number. A component of a digit is also called it's divisor.
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