Question

isaiah wants to write 1,040 as a product. he says he can write 10 as a factor twice because two of the digits in 1,040 are 0. is isaiah correct? because 0? indicate 10 as a factor. incorrect correct

Explanation:

Step1: Recall the concept of factoring

To write a number as a product of factors, we use the rules of multiplication.

Step2: Analyze 1040

We find the prime - factorization of 1040. \(1040=2\times520 = 2\times2\times260=2\times2\times2\times130=2\times2\times2\times2\times65=2\times2\times2\times2\times5\times13\). Also, \(1040 = 10\times104=10\times2\times52 = 10\times2\times2\times26=10\times2\times2\times2\times13\). We can write \(1040 = 10\times104\), and \(104 = 10\times10.4\) is not an integer - factorization. The correct way to express 1040 in terms of factors of 10 is \(1040=10\times104\), not as \(10\times10\times\) (some integer). Isaiah is incorrect.

Answer:

No, Isaiah is incorrect. Just because two digits in 1040 are 0 does not mean 10 can be written as a factor twice in an integer - factorization of 1040. The prime - factorization of 1040 is \(2^{4}\times5\times13\), and \(1040 = 10\times104\) where \(104\) is not a multiple of 10.