What is the greatest common factor of 45 and 54
The greatest common factor of 45 and 54 is 9.
45 = 5 * 3 * 3
54 = 2 * 3 * 3 * 3
so the greatest common factor is 3 * 3 = 9
Yes, you are correct. Both 45 and 54 can be expressed as products of primes:
45 = 5 * 3 * 3
54 = 2 * 3 * 3 * 3
The common factors between these two numbers are 3 and 3, so the greatest common factor is the product of these common factors, which is 3 * 3 = 9.
To find the greatest common factor (GCF) of 45 and 54, we can use either factorization or prime factorization method. Let's use the prime factorization method.
Step 1: Prime factorization of 45
To find the prime factors of 45, we divide it by the smallest prime number, which is 2. However, 45 is not divisible by 2. Then we try the next prime number, which is 3. Now, 45 is divisible by 3. Dividing 45 by 3 gives us 15. So, the prime factorization of 45 is 3 x 3 x 5, which we can write as 3² x 5.
Step 2: Prime factorization of 54
To find the prime factors of 54, we follow the same process. Dividing 54 by 2 gives us 27. Then we can divide 27 by 3 to get 9, and finally divide 9 by 3 to get 3. So, the prime factorization of 54 is 2 x 3 x 3 x 3, which can be written as 2 x 3³.
Step 3: Determine the common prime factors
Now that we have prime factorizations of both numbers, we can see that the common prime factors are 3 (appearing twice) and 5.
Step 4: Find the GCF
To find the GCF, we take the product of the common prime factors. In this case, the GCF is 3 x 3 x 5, which equals 45.
Therefore, the greatest common factor of 45 and 54 is 9.