USING PRIME FRACTORIZATION WHAT IS THE GCF FOR 45,100 USING A FACTOR TREE AND COMMON PRIME FACTORS
here is the easiest way,
45 = 3*3*5
100 = 2*2*5*5
so the GCF is 5
To find the GCF (Greatest Common Factor) of 45 and 100 using prime factorization, we can start by finding the prime factorizations of both numbers.
Step 1: Prime Factorization of 45
To find the prime factorization of 45, we can use a factor tree. Start by dividing 45 by the smallest prime number, which is 2. Since 45 is an odd number, we can continue dividing by the next prime number, which is 3.
45
/ \
3 15
/ \
3 5
The prime factorization of 45 is 3 * 3 * 5, which can also be written as 3^2 * 5.
Step 2: Prime Factorization of 100
To find the prime factorization of 100, divide it by the smallest prime number, which is 2.
100
/ \
2 50
/ \
2 25
/ \
5 5
The prime factorization of 100 is 2 * 2 * 5 * 5, or 2^2 * 5^2.
Step 3: Common Prime Factors
To find the GCF, we need to identify the common prime factors of 45 and 100. From their prime factorizations, we can see that both numbers have 2 and 5 as prime factors.
Step 4: GCF Calculation
To calculate the GCF, we take the product of the common prime factors raised to the lowest exponent. In this case, the common prime factors are 2 and 5.
Since 2^2 and 5^1 are the lowest exponents for these prime factors, the GCF is 2^2 * 5^1 = 20.
Therefore, the GCF of 45 and 100, using prime factorization and common prime factors, is 20.