Is the number 1,200 divisible by 5? Can the first number be divided evenly by the second (without a remainder)? Compare the prime factorizations of the two numbers

Is the number 1,200 divisible by 5?

Method 1. The division of the two numbers:

A natural number 'A' could only be divisible by another number 'B' if after dividing 'A' by 'B' the remainder was zero.


1,200 would be divisible by 5 only if there was a natural number 'n', so that:
1,200 = 'n' × 5


If we divide the two numbers, the remainder is zero:


1,200 ÷ 5 = 240 + remainder 0


=> 1,200 = 240 × 5


=> The number 1,200 is divisible by 5.


5 is a factor (divisor) of the number 1,200:


5 | 1,200


The abbreviation 5 | 1,200 means that the number 5 is a factor (divisor) of the number 1,200.


1,200 is a multiple of the number 5.


The number 1,200 is divisible by 5:
5 | 1,200

Method 2. The prime factorization of the numbers:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


1,200 = 24 × 3 × 52
1,200 is not a prime number but a composite one.


5 is a prime number and cannot be broken down into other prime factors.



* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.


1,200 contains all the prime factors of the number 5.


=> The number 1,200 is divisible by 5:


5 | 1,200


The abbreviation 5 | 1,200 means that the number 5 is a factor (divisor) of the number 1,200.


5 is a factor (divisor) of the number 1,200.


1,200 is a multiple of the number 5.

The number 1,200 is divisible by 5:
5 | 1,200


The final answer:
(scroll down)

The number 1,200 is divisible by 5:
5 | 1,200.
The two numbers divide without a remainder.
1,200 contains all the prime factors of the number 5.
5 is a factor (divisor) of the number 1,200.
1,200 is a multiple of the number 5.

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The divisibility of the natural numbers:

Method 1: Divide the numbers and check the remainder of the operation. If the remainder is zero, then the numbers are divisible.

Method 2: The prime factorization of the numbers (the decomposition of the numbers into prime factors).

1. What is the numbers' divisibility? 2. Divisibility rules. 3. Calculating the divisors (factors). 4. Quick ways to determine whether a number is divisible by another one or not.


What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

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