Is the number 777 divisible by 3? Can the first number be divided evenly by the second (without a remainder)? Compare the prime factorizations of the two numbers

Is the number 777 divisible by 3?

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.


777 would be divisible by 3 only if there was a natural number 'n', so that:
777 = 'n' × 3


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


777 ÷ 3 = 259 + 0;


=> 777 = 259 × 3;


=> The number 777 is divisible by 3.


3 is a factor (divisor) of the number 777:


3 | 777


The abbreviation 3 | 777 means that the number 3 is a factor (divisor) of the number 777.


777 is a multiple of the number 3.


The number 777 is divisible by 3:
3 | 777

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.


777 = 3 × 7 × 37
777 is not a prime number but a composite one.


3 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.


777 contains all the prime factors of the number 3.


=> The number 777 is divisible by 3:


3 | 777


The abbreviation 3 | 777 means that the number 3 is a factor (divisor) of the number 777.


3 is a factor (divisor) of the number 777.


777 is a multiple of the number 3.

The number 777 is divisible by 3:
3 | 777

The final answer:
The number 777 is divisible by 3:
3 | 777.
The two numbers divide without a remainder.
777 contains all the prime factors of the number 3.
3 is a factor (divisor) of the number 777.
777 is a multiple of the number 3.

Other operations of this type:

Is the number 777 divisible by 118?

Calculator: Are the two numbers divisible?

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).

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