Prime Factorization of 105
Find the prime factorization of 105. Express 105 as a product of prime numbers.
To find the prime factorization of 105, we need to express it as a product of prime numbers.
We do this by repeatedly dividing by the smallest prime that divides evenly, starting with 2.
A prime number is only divisible by 1 and itself (2, 3, 5, 7, 11, 13, ...).
105 is an odd number, so it is not divisible by 2.
We move on to check the next prime number: 3.
3 is a prime number that divides our current value. We can divide by 3 once:
After dividing by 3, we have 35 remaining.
5 is a prime number that divides our current value. We can divide by 5 once:
After dividing by 5, we have 7 remaining.
We are left with 7, which is greater than 1.
7 cannot be divided by any prime smaller than its square root.
Therefore, 7 is itself a prime number and is our final factor.
Now we combine all the prime factors we found:
Expanded form: 105 = 3 × 5 × 7
Exponential form: 105 = 3 × 5 × 7
We can verify: 3 × 5 × 7 = 105 ✓