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All numbers that have 3 and 13 as factors are multiples of the LCM of 3 and 13 which is 39.
The 4 digit numbers are 1000 to 9999 and of these, the multiples of 39 are:
1000 ÷ 39 = 2525/39 ⇒ first multiple of 39 greater than or equal to 1000 is 26 x 39 = 1014
9999 ÷ 39= 25615/39 ⇒ last multiple of 39 less than or equal to 9999 is 256 x 39 = 9984
Thus the multiples from 26 to 256 of 39 are the 4 digit numbers with 3 and 13 as factors.
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878 three digit numbers have an even number of factors. Every factor of a number has a pair, so there ought to be an even number of factors for every number. However, if a pair of the factors are the same number, then there will be an odd number of factors, that is if the number is a perfect square. Assuming three digit numbers are 100 to 999: From 100 to 999, the perfect squares are 102 = 100 to 312 = 961, a total of 31-10+1 = 22 numbers. So of the 999-100+1 = 900 three digit numbers, 22 have an odd number of factors, so 900-22 = 878 have an even number of factors.
The 3 digit numbers under 500 are 100 through 499.
The factors of 39 are the numbers that can be evenly divided into 39 without leaving a remainder. The factors of 39 are 1, 3, 13, and 39. The prime factors of 39 are the prime numbers that multiply together to give the original number. In this case, the prime factors of 39 are 3 and 13.
999-111=888 888 3 digit numbers can be made with numbers between 1 - 9
prime numbers of 234 = 2, 3, 13