Question

find the number of divisors of 1420

Answer 1

\(\normalsize\color{black}{ 1420=20 \times 71 }\)
\(\normalsize\color{black}{ 1420=2 \times 2 \times 5 \times 71 }\)

Answer 2

71 is prime

Answer 3

prime divisors are 2,5,71
divisors are 2,4,5,10,20,71,142,284,355,710

Answer 4

Find the divisors of the following:
\[1420 \]Perform the prime factorization of 1420:
\[1420 = 2^2×5×71 \]Gather all factors of 1420 through its prime factorization:
\[2^0×5^0×71^0 \]\[2^1×5^0×71^0 \]\[2^2×5^0×71^0 \]\[2^0×5^1×71^0 \]\[2^1×5^1×71^0 \]\[2^2×5^1×71^0 \]\[2^0×5^0×71^1 \]\[2^1×5^0×71^1 \]\[2^2×5^0×71^1 \]\[2^0×5^1×71^1 \]\[2^1×5^1×71^1 \]\[2^2×5^1×71^1 \]Evaluate:
\[2^0×5^0×71^0 = 1 \]\[2^1×5^0×71^0 = 2 \]\[2^2×5^0×71^0 = 4 \]\[2^0×5^1×71^0 = 5 \]\[2^1×5^1×71^0 = 10 \]\[2^2×5^1×71^0 = 20 \]\[2^0×5^0×71^1 = 71 \]\[2^1×5^0×71^1 = 142 \]\[2^2×5^0×71^1 = 284 \]\[2^0×5^1×71^1 = 355\]\[2^1×5^1×71^1 = 710\]\[2^2×5^1×71^1 = 1420 \]

Answer 5

number of divisors of \(\large 1420 = 2^{\color{red}{2}}\times5^{\color{red}{1}}\times 71^{\color{red}{1}} \)

can be given by : \(\large \color{Red}{(2+1)(1+1)(1+1) = (3)(2)(2) = 12}\)

Answer 6

ya shorrt cut

Answer 7

not exactly a shortcut,
you're just calculating number of possible combinations

Answer 8

ok