How to Find the Factors of 144?
Factor, in arithmetic, is a number or algebraic expression that divides every quantity or expression (of which it is a factor) uniformly, which means without any remainder. For example, 4 and 2 are factors of 8, when multiplied together, the result is 8.
Similarly, factors of 144 would be all the pairs of numbers, which, when multiplied together, give the result as 144. Now the question that arises is what the factors of 144 and how to find them are?
To start with, the factors of 144 are 1, 4, 2, 3, 6, 8, 16, 9, 12, 18, 24, 36, 48, 72 and 144. Now that the 'what are the factors of 144' is solved, the next step would be to figure out how to find these factors, and there are various methods to figure out a number's factors, such as:
Prime Factorization of 144
Prime Factorization of 144 by division method is the first way to calculate a number's factors.
We'll start by dividing the number, i.e., 144 by the smallest integer, which is 2.
The process will start with, 144 ÷ 2 = 72
Then, 72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
Now that two can't be divided with nine further without getting a decimal number, we'll move onto the next integer, that is, 3.
Now, 9 ÷ 3 = 3
And, 3 ÷ 3 = 1
Prime Factorization Explained Through Diagrammatic Means
144 =
2 |144
2 |72
2 |36
2 |18
3 |9
3 |3
1
144 = 2 x 2 x 2 x 2 x 3 x 3
When the final outcome is 1 that is when we stop the division process as we can't go further than this. So, the prime factors of 144 are written in a format of 2 x 2 x 2 x 2 × 3 x 3 or 24 x 32, where 2 and 3 are the prime numbers.
Similarly, we can group two numbers which when multiplied together gives us the result as 144, which is also called Pair Factors.
Pair Factors Method
What are the Factors of 144?
When calculated and counted, we concluded that the number 144 has 15 positive as well as 15 negative factors. Thus, there are 30 factors of 144 in total.
Exponential Form of 144
The exponential form is a compact way of representing a number. For example, instead of writing 2 × 2 × 2 × 2 = 16, we can always express it as 24.
Similarly, the prime factorization of 144 using exponents would be, 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32.
Fun Facts
144 is a composite number as well as a perfect square. 144 could also be called a dozen dozens as well as it is 1 x 12. Another fact is that 144 is a perfect square as the square root of the number 144 is 12. Thus, the square root of 144 is an integer and 144 is a perfect square.
144 is a perfect square, yes, but the sum of its digits is also a perfect square, i.e., 9 (1 + 4 + 4 ), the product of its digits is also a perfect square, i.e.16, and its reverse is also a perfect square, i.e., 441.
From our context, we got to learn the following things on the factors of 144:
Factor Pairs: 144 = 1 x 144, 3 x 48, 2 x 72, 4 x 36, 8 x 18, 6 x 24, 9 x 16, 12 x 12.
Factors of 144: 1, 4, 2, 3, 6, 8, 16, 9, 12, 18, 24, 36, 48, 72, 144.
Prime Factorization: 144 = 2 x 2 x 2 x 2 x 3 x 3.
Prime Factorization of 144 using Exponents: 2 x 2 x 2 x 2 × 3 x 3 = 24 × 32
FAQs on Factors of 144
1. What are the Types of Factoring Methods?
Four types of factoring methods:
GCF, Greatest Common Factor – is the largest positive integer that divides uniformly into all numbers with zero as the remainder. E.g., 6 is the Greatest Common Factor of 18, 30 and 42
Difference in two squares - In arithmetic terms, the distinction of squares is a squared quantity subtracted from another squared quantity. E.g., the theorem of (a + b)(a - b) = a² - b²
The Sum or Difference in 2 cubes - The sum or the difference present between two cubes can be factored into a specific product. E.g., the theorem of sum;
(a + b)( a2 − ab + b2) = a3 + b3 , the theorem of difference; (a − b)(a2 + ab + b2) = a3 − b3
Trinomials - In the form of x2 + bx + c can regularly be factored because it is the product of two binomials. Understand that a binomial is really a two-term polynomial. E.g, the trinomial theorem; ax2 + bx + c.
2. What is an Easy Way to Find Factors of a Number?
The method of prime factorization by division method would be the easiest way out, to identify all the factors of a number. You just have to start dividing your number with the smallest integer, i.e., two and take the process further till it can't be divided by 2, then you have to start with next smallest, i.e., 3 and the process will go like this till you get 1 as the remainder. If the number doesn’t get divided by 2 in the first place, try dividing it with 3,or 4, and so on...
3. How do you explain factors to students initially?
Every time when you try to introduce a new concept try to understand its entire details with respect to definition, formulas, and everything. Here, a factor is one of two or more numbers that divides a given number without a remainder. The terms Multiples and factors are best explained by using a particular number sentence which will be as the following where this number sentence tells us that 20 is a multiple of 5 and is also a multiple of 4. It also explains to us that 5 and 4 are factors of 20.
4. How to Find Factors of the Number 144?
Find all the numbers less than or equal to the number 144. Then divide the given number by each of the numbers found. After dividing them the divisors that give the remainder when divided to be 0 are the factors of the number 144. It is usually easy to find factors of any small number rather than finding it for a bigger longer number. It requires knowledge in multiplication and division as well.
5. What is the easiest way to find Factors?
Every student must learn how the concept actually works. They need to be very sure of their multiplication and division methods followed without any calculators. The quickest way to find the factors of a number is to divide it by the smallest prime number which is bigger than 1 and a number that goes into it evenly with no remainder. Continue this definite process with each number you get, until you reach and obtain number 1.
6. What are the factors of the number 144 in Mathematics?
Every individual number will have a different amount of factors found depending on the type of number they are. Here the number 144 has 15 factors totally.
Factor Pairs: 144 = 1 x 144, 3 x 48, 2 x 72, 4 x 36, 8 x 18, 6 x 24, 9 x 16, 12 x 12.
Factors of 144: 1, 4, 2, 3, 6, 8, 16, 9, 12, 18, 24, 36, 48, 72, 144.
Likewise, factors of other numbers also can be found easily through simple division and multiplication techniques.
7. What is a prime factor in Mathematics?
Prime factorization is a particular way of expressing any number as a product of its given prime factors. And a prime number is a number that has exactly two main factors, 1 and the number itself. Prime factors are factors of a number that are themselves prime numbers. There are many methods to find and obtain the prime factors of a number, but one of the most common is to use the prime factor tree method. In other words: any of the prime numbers can be multiplied to give the original number.
For Example: The prime factors of 15 are 3 and 5 (because 3 * 5 =15, and 3 and 5 are prime numbers).