Why & How does Divisibility Rule for 25 Work? | Divisibility Test of 25 Proof with Example
Excited to learn what is the divisibility rule for 25 along with how it works and practice with some solved examples? Then, let’s start gaining knowledge about the rule of divisibility for 25 before we see why we use the divisibility test. Divisibility test rules of 25 are used to determine whether the numbers are divisible by 25 or not in a simple process without performing division methods. From here you are going to study what is the rule of 25 divisibility, how to check if the number is divisible by 25 or not, and divisibility by 25 proof with example.
What is the Divisibility Rule of 25?
The divisibility rule of 25 says if the number is divisible by 25 exactly when the last two digits formed are 0 or divisible by 25. Want to see the proof of the divisibility rule for 25? Check the below module.
Divisibility Test for 25 Proof
When the number is divisible by 25 then the last two digits should be divisible by 25 and the numbers are 00, 25, 50, or 75.
Proof:
If you consider 5150 as an example number then prove if it is divisible by 25 or not.
First, we assume this number to be written as
5150 = 5*1000 + 1*100 + 5*10 + 0
We can prove it depends on the below observation:
Remainder of 10i divided by 25 is 0 if ‘i’ greater than or equal to two.
Later state that 100, 1000,... etc lead to a remainder of 0 when divided by 25.
Thus, remainder of " 5*1000 + 1*100 + 5*10 + 0" divided by 25 is equivalent to remainder
of following :
0 + 0 + 50 + 0 = 50
Since 50 is divisible by 25, hence proved.
Solved Examples on Divisibility by 25
Example 1:
Is 4525 divisible by 25?
Solution:
Given number is 4525
To check whether it is divisible by 25, you need to consider the last two digits of the number and it should be zero or divisible by 25.
Here, the last two digits of the given number are 25
25 is divisible by 25
Hence, 4525 is divisible by 25.
Example 2:
Is 5678 divisible by 25?
Solution:
Given input is 5678
Divisibility rule of 25 states that when the last two digits formed are 00, 25, 50, and 75 then it is divisible by 25.
Here, the last two digits are 78 which is not divisible by 25.
Thus, 5678 is not divisible by 25.
What numbers are divisible by 25
List of Numbers divisible by 25: The Numbers 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200, 1225, 1250, 1275, 1300, 1325, 1350, 1375, 1400, 1425, 1450, 1475, 1500, 1525, 1550, 1575, 1600, 1625, 1650, 1675, 1700, 1725, 1750, 1775, 1800, 1825, 1850, 1875, 1900, 1925, 1950, 1975, 2000, 2025, 2050, 2075, 2100, 2125, 2150, 2175, 2200, 2225, 2250, 2275, 2300, 2325, 2350, 2375, 2400, 2425, 2450, 2475, 2500, etc. are divisible by 25.
FAQs on How To Tell If A Number is Divisible by 25?
What are the numbers divisible by 25?
The numbers that are divisible by 25 starts from the lowest number which is itself 25 ie., 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, etc.
Why does the divisibility test for 25 work?
As per the divisible rule for 25, the number is exactly divisible by 25 when the last two digits of a number are zeroes or the number formed by the last two digits is a multiple of 25.
Is a number that is divisible by 25 also divisible by 5?
Yes, all of the numbers which are divisible by 25 fully are also divisible by 5.
Wrapping Up
We desire the information shared above regarding the divisibility rule for 25 helped you in assisting while solving the division of large numbers by 25. For more details like this, you have to visit our site Roundingcalculator.guru and get them free in a matter of seconds. Also, you may clarify all your ambiguities about Divisibility Rules and many more concepts in no time.
