Factors of 625: Prime Factorization, Methods, Tree, and Examples

Factors of 625 can be found out as when any two numbers multiplied together give the number 625 as a product or when the number 625 is divided by another number and it provides zero remainders then it is called a factor of the number 625.Every number has both positive factors and negative factors. We can exclude the negative factors if we want to. A factor always has to be a whole number and never in fraction or decimal format.The number 625 has in total 10 factors, out of which only 5 factors are positive. In this article, you can learn about all of the Prime Factors, Factor tree, fun facts, and tricks to solve questions related to the factors of 625.

What are the Factors of 625?

The factors of 625 are 1, 5, 25, 125, and 625 as an integer that divides 625 to give 0 as a reminder and a whole number as a quotient will be listed as a factor of 625.

Any number that ends with the number 5 will have 5 as a factor. 625 is an odd and composite number. So by dividing the number 625 by other numbers we can form the list. \[Factors\ of\  625 = 1, 5, 25, 125, 625 \]

How To Calculate the Factors of 625?

As \[Factors\ of\ 625 = 1, 5, 25, 125, 625 \]Similarly, the negative factors list is as follows\[Factors\ of\ 625 = -1,- 5,- 25, -125,- 625 \]We can also state its prime factors which are as below  To find the all of factors of 625 we will follow these steps:Divide the number 625 by the smallest number i.e 1.\[ \dfrac{625}{1}=625, remainder = 0\]This is the main method to find the factors of 625 or any number. This is called the basic division method.Now we will find it for other numbers\[ \dfrac{625}{5}=125, remainder = 0\] \[ \dfrac{625}{25}=25, remainder = 0\] \[ \dfrac{625}{125}=5, remainder = 0\]\[ \dfrac{625}{625}=1, remainder = 0\] Since no further factors are present we can say that,\[Factors\ of\  625 = 1, 5, 25, 125, 625 \]We can also determine the factors of 625 by finding any two numbers whose product will give us 625 as an answer.Like,\[1\times 625 = 625 \]We can use the multiplication method as an alternative for finding Factors.Here are some Fun Facts about the number 625 and its factors:

1. The number 625 itself is composite
2.  It is a perfect square of 25
3.  625 is also a perfect fourth power 
4. The Prime Factorisation exponent of 625 is 4
5. There are only two-three digits factors i.e 125 and 625
6. 625’s additive inverse is its negative factor which is -625
7. Along with every other number, 1 is also a factor of 625

Factors of 625 by Prime Factorization

Prime factors of 176 are all those numbers that can only be divided by 1 and that number itself. Hence these factors, when multiplied answer 625. It can be done in 2 different ways Prime FactorisationTo find the prime factors you can follow the steps given below:Choose the smallest prime number factor i.e 5Note that zeros and 1s are not considered prime numbers so we will not include themThen Divide 625 by 5 \[ \dfrac{625}{5}=25, remainder = 0\] Further, divide the answer with the number 5 \[ \dfrac{125}{5}=125, remainder = 0\] We will keep on dividing the answer until we get a remainder in the answer\[ \dfrac{25}{5}=5, remainder = 0\] As we know that a remainder indicates that the number is not a factor of the given number.Since the answer is not further divisible by 5 without giving a remainder we will shift to the next prime number and will keep on repeating the steps until we get 1 in the answer.\[ \dfrac{5}{5}=1, remainder = 0\] We can summarize all of the prime factors as\[5 \times 5 \times \times 5 \times 5 = 625 \]

Factor Tree of 625

It is a way to illustrate the prime factors of a number and the factors of those numbers too. We can make a factor tree to understand the prime factorization even more. For that, we must clarify our concept of prime factors.In total, we have 4 prime factors of 625 which are 5,5,5 and 5.The diagram given below is called a factor tree.

Factors of 625 in Pairs

A factor pair is the product of two numbers that gives that certain number. For the number 625, we will find factor pairs by multiplying any two factors to give 625 as an answer. For positive factors we can find pairs in this way:\[1\times 625 = 625 \]\[5\times 125 = 625 \]\[25\times 25 = 625 \]Note that each number when multiplied by each other gives 625 in the answer which tells that they are the positive factor of 625.Now for the negative factors of 625, we can also find the factor pairs. \[-1\times -625 = 625 \]\[-5\times -125 = 625 \]\[-25\times -25 = 625 \]Since two times minus will cancel out each other so we will get the negative pair factorSo we can write the pairs in this way as given below.\[Positive\ Factor\ Pair\ of\ 625 = (1, 625), (5, 125), (25, 25)\]\[Negative\ Factor\ Pair\ of\ 625 = (-1,- 625), (-5, -125), (-25, -25) \]

Factors of 625 Solved Examples

Example 1

What are the common factors of 625 and 25

Solution

Factors of 25 are 1, 5,25Whereas,\[Factors\ of\  625 = 1, 5, 25, 125, 625 \]So the common factors of 25 and 625 are 1,5,25

Example 2

List all of the negative factors of 625 and the prime factors

Solution

Factors of 625 are the numbers that divide to give zero remainders when 625 is the dividend.So,\[Factors\ of\  625 = 1, 5, 25, 125, 625 \]Prime Factors of 625 are:\[5 \times 5 \times \times 5 \times 5 = 625 \]

Example 3

Miss Julia is a teacher. She has 25 students in her class. For an art project, she has 625 pencils. Can you help Miss Julia to divide the 625 pencils among her class so that everyone gets an equal number of pencils?

Solution

We will use the Factors concept to divide all the pencils. As 625 is a multiple of 25 so we can divide the pencils equally by finding the factor pair of 625 which includes 25 which is\[25\times 25 = 625 \] Images/mathematical drawings are created with GeoGebra. <

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