find the gcf and lcm of 315 and 882.
To find the greatest common factor (GCF) and least common multiple (LCM) of two numbers, we can use a step-by-step approach.
Step 1: Prime Factorization
We start by finding the prime factorization of both numbers.
Prime factorization of 315:
315 = 3 * 3 * 5 * 7
Prime factorization of 882:
882 = 2 * 3 * 3 * 7 * 7
Step 2: GCF
To find the GCF, we need to identify the common prime factors between the two numbers and multiply them together.
Common prime factors: 3 and 7
GCF = 3 * 7 = 21
Step 3: LCM
To find the LCM, we need to identify all the unique prime factors from both numbers and multiply them together.
Unique prime factors: 2, 3, 3, 5, and 7
LCM = 2 * 3 * 3 * 5 * 7 = 630
So, the GCF of 315 and 882 is 21, and the LCM is 630.