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All numbers have factors. Some numbers have some of the same factors as other numbers. Multiples of numbers have all of the factors of numbers that are factors of them, plus some of their own. 32 is a multiple of 16 and will have all of its factors. 64 is a multiple of both 32 and 16 and will have all of their factors.
The factors of 16 are: 1, 2, 4, 8, 16.
Because 16 is a factor of 48.
The number of factors of a number is calculated as the product of the powers of the number written in power format increased by 1. As there are required to be 5 factors, and as 5 is a prime, it can only be achieved if the number has a prime factorisation which is a single prime raised to the 4th power. The smallest prime is 2, and 2⁴ = 16 The next prime is 3, and 3⁴ = 81 which is too big. → the required number is 16 (which has the 5 factors 1, 2, 4, 8, 16).
Divide the number 32 by successive prime numbers to get the factors until you cant divide any more numbers... 32/1=32 (factors are 1 and 32) 32/2=16 (factors are 2 and 16) 32/3=does not divide to be a whole number 32/4=8 (factors are 4 and 8) 32/5=does not divide to be a whole number 32/6=does not divide to be a whole number 32/7=does not divide to be a whole number Now you done with all the numbers you can. Therefore 1,32,2,16,4 and 8 are factors.