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

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## Answers ( 5 )

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

Greatest common factors of 9 and 18

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

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 .