To find out the number of multiples of 360, let's first find out its factors and then take them out of the total factors. This will ensure that the remaining factors will always include the factors of 360.
Let's solve now:
360 = 9 * 4 * 10 =\(3^2*2^3*5^1\)
That means let's take two 3s, three 2s and one 5 out of the originalnumber.
\(2^6*3^5*5^4*6^3\)
After taking the required factors out, we are left with :\(2^3*3^3*5^3*6^3\)
As per the formula,\(a^p*b^q*c^r\) , we have number of factors = (p+1)(q+1)(r+1),
...
Let's solve now:
360 = 9 * 4 * 10 =\(3^2*2^3*5^1\)
That means let's take two 3s, three 2s and one 5 out of the originalnumber.
\(2^6*3^5*5^4*6^3\)
After taking the required factors out, we are left with :\(2^3*3^3*5^3*6^3\)
As per the formula,\(a^p*b^q*c^r\) , we have number of factors = (p+1)(q+1)(r+1),
...
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