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Number Theory Level pending

How many factor of this number??

277200 \LARGE 277200


The answer is 180.

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2 solutions

Munem Shahriar
Nov 25, 2017

Step 1: Prime factorization

277200 = 2 4 × 3 2 × 5 2 × 7 × 11 277200 = 2^4 \times 3^2 \times 5^2 \times 7 \times 11

Step 2: Apply divisor formula

( 4 + 1 ) ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 180 Divisors (4+1)(2+1)(2+1)(1+1)(1+1) = \boxed{180} ~ \text{Divisors}

Md Mehedi Hasan
Nov 25, 2017

We can write that, 277200 = 2 4 3 2 5 2 7 11 277200=2^4\cdot3^2\cdot5^2\cdot7\cdot11

So the number of factors are = ( 4 + 1 ) ( 2 + 1 ) ( 2 + 1 ) 2 2 = 180 =(4+1)(2+1)(2+1)2^2\\=\boxed{\color{#3D99F6}180}

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