## What Is The Greatest Common Factor Of 9 And 18?

Question

Do you know the common factor of 9 and 18?

0

1. The common divisors of the numbers 9 and 18
Divide the larger number by the smaller.
Please note that when numbers are divided, the remainder is zero:
18:9 = 2 + 0
=> 18 = 9 × 2
=> Thus, 18 is divisible by 9.
=> 9 is a divisor of 18.
The greatest common divisor:
gcd(9;18) = 9
>> The greatest common divisor

2. gcd(9;18)=? Calculate the greatest common divisor of numbers, gcd, by two methods: 1) Divisibility of numbers and 2) Decomposition into prime factors (prime factorization)

Method 1. The divisibility of numbers:
Divide the larger number by the smaller.
Please note that when numbers are divided, the remainder is zero:
18:9 = 2 + 0
=> 18 = 9 × 2
So 18 is divisible by 9.
And 9 is a divisor of 18.
The greatest common divisor:
gcd(9;18) = 9

gcd(9;18)=9=32
18 is divisible by 9

Method 2. Decomposition into prime factors (prime factorization):
The decomposition into prime factors (the prime factorization) of a number: find the prime numbers that multiply together to form this number.
9 = 32
9 is not a prime number but a compound.
18 = 2×32
18 is not a prime number but a compound.
* Natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two divisors: 1 and itself.
* A composite number is a natural number that has at least one divisor other than 1 and itself.

>> Decomposition into prime factors (prime factorization)
Multiply all the common prime factors, taken by their smallest powers (exponents).
gcd(9;18) = 32

3. What are all the divisors of 18?

Regarding 18 , the answer is: No, 18 is not a prime number. The list of its integer divisors (that is, the list of integers that divide 18 ) is as follows: 1, 2, 3, 6, 9, 18 . For 18 to be a prime number, 18 would have to be divisible only by itself and 1.

How to find a divisor of 18?

How to be sure that the number 2 is a divisor of 18 ? 2 is a divisor of 18 only if you get a whole number when you divide 18 by 2. 9 is one is not a decimal digit, so 2 and 9 are both divisors of 18 .