Question

How do you express 3080 as a product of prime factors?

Answer 1

Hint: We will first observe that it is an even number, therefore, will be divisible by 2 and thus the same will happen again. After that we will just keep on checking the smallest prime number it can be divided with.

Complete step-by-step solution:
We are given that we need to express 3080 as a product of prime factors.
Since, we can observe that 3080 is an even number, therefore, it is definitely divisible by 2.
Now, we can write 3080 as the multiple of 2 and 1540 which means $3080 = 2 \times 1540$........…….(1)
Now, we can observe that 1540 is an even number, therefore, it is definitely divisible by 2.
Now, we can write 1540 as the multiple of 2 and 770 which means $1540 = 2 \times 770$..........……(2)
Putting equation number (2) in equation number (1), we will then obtain the following equation:-
$ \Rightarrow 3080 = 2 \times 2 \times 770$........………….(3)
Now, we can observe that 770 is an even number, therefore, it is definitely divisible by 2.
Now, we can write 770 as the multiple of 2 and 385 which means $770 = 2 \times 385$ ……(4)
Putting equation number (4) in equation number (3), we will then obtain the following equation:-
$ \Rightarrow 3080 = 2 \times 2 \times 2 \times 385$ ………….(5)
Now, we can observe that 385 has 5 at the end, therefore, 385 is divisible by 5.
Now, we can write 385 as the multiple of 5 and 77 which means $385 = 5 \times 77$ ……(6)
Putting equation number (6) in equation number (5), we will then obtain the following equation:-
$ \Rightarrow 3080 = 2 \times 2 \times 2 \times 5 \times 77$ ………….(7)
Now, we can observe that 77 is multiple of 7 and 11 which means $77 = 7 \times 11$ ……(8)
Putting equation number (8) in equation number (7), we will then obtain the following equation:-
$ \Rightarrow 3080 = 2 \times 2 \times 2 \times 5 \times 7 \times 11$

Thus, the prime factorization of 3080 is $2 \times 2 \times 2 \times 5 \times 7 \times 11$.

Note: The students must note that there are divisibility rules to check whether a number is divisible by some number or not.
For instance:- If we have to check if any number is divisible by 2, we just have to look at the last digits, if that is divisible by 2, then the number is itself divisible by 2 as well.
We have a rule for 3 as well, we sum all the digits of the given number and then check if that is divisible by 3, if that is divisible by 3, which means the given number is divisible by 3.