Numbers: Find the number of divisors of 600
Method:
Find the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.
Example:
Find the number of divisors of 600
Solution:
Prime Factorization of 600:
2 | 600
2 | 300
2 | 150
3 | 75
5 | 25
5 | 5
| 1
2^3, 3^1 & 5^2
Exponents: 3, 1 & 2
Add 1 to each exponent = (3+1) (1+1) (2+1)
Multiple “exponents+1” together = (3+1) x (1+1) x (2+1) = 4 x 2 x 3 = 24
Total number of divisors of 600 = 24
Method:
Find the prime factorization of the number n.
Take all the exponents in the factorization.
Add 1 to each
Then multiply these "exponents + 1"s together.
Example:
Find the number of divisors of 600
Solution:
Prime Factorization of 600:
2 | 600
2 | 300
2 | 150
3 | 75
5 | 25
5 | 5
| 1
2^3, 3^1 & 5^2
Exponents: 3, 1 & 2
Add 1 to each exponent = (3+1) (1+1) (2+1)
Multiple “exponents+1” together = (3+1) x (1+1) x (2+1) = 4 x 2 x 3 = 24
Total number of divisors of 600 = 24
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