how many factors does 144 have

how many factors does 144 have It depends on how we are counting prime factors If you are in a class the instructor may have already talked about how they want you to count them 144 2 xx 2 xx 2 xx 2 xx 3 xx 3 144 has two distinct or two different prime factors Without the word distinct or different or something else to indicate how to count I would say 144 has

The prime factors are only 2and 3 As the product of prime factors 144 2xx2xx2xx2xx3xx3 The question is not very clear The prime factors of 144 are only 2 and 3 However if the intention of the question was to write 144 as the product of its prime factors we would have the following 144 12xx12 16xx9 24xx6 etc 144 5 and 29 Factors are the smallest integers that can be combined by multiplication to obtain the original value They are all therefore prime numbers They are extremely useful in mathematics in simplifying problems by finding least and greatest common denominators To factor 145 it is useful to note that it ends with a 5 thus 5 is

how many factors does 144 have

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1 2 17 and 34 By definition a is a factor of b or a b iff and only if there exists an integer k in ZZ such that b a k or b ka In other words b a leaves a zero remainder In particular then the factors of 34 are all natural numbers that can divide into 34 without leaving a remainder In other words all a such that 34 a in ZZ So therefore the factors How many factors does 144 have What is 15 36 divided by 4 8 How are factors and products related

For numbers greater than 8 to be factors of 40 they would have to be multiplied by something less than the 5 we use in 8xx5 40 We ve already checked the smaller numbers so we re done The factors are 1 2 4 5 8 10 20 40 All non zero numbers are divisors of 0 0 may also be counted as divisor depending on whose definition of divisor you use This answer assumes the following definition of divisor For integers m n we say that m is a divisor of n and write m n if and only if there is some integer k such that km n If n is any number then n xx 0 0 So n

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249 This product is commonly known as the factorial of 1000 written 1000 The number of zeros is determined by how many times 10 2xx5 occurs in the prime factorisation of 1000 There are plenty of factors of 2 in it so the number of zeros is limited by the number of factors of 5 in it These numbers have at least one factor 5 5 10 15 1 2 4 8 16 32 64 Factoring 64 into primes we find that it is a power of 2 64 2 xx 32 2 xx 2 xx 16 2 xx 2 xx 2 xx 8 2 xx 2 xx 2 xx 2 xx 4 2 xx 2 xx 2 xx 2 xx 2 xx 2 2 6 So the only possible positive factors of 64 are powers of

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