1.how many two-digit primes are there whose units digit is more than its tens digit ?
Here they all are. You count them:
13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89
2.how many four-digit numbers are multiples of 15 ?
The smallest 4-digit number is 1000, divide 1000 by 15, get 66.666...
So take the next integer 67. Multiply it by 15 and get 1005, which
is the smallest 4-digit multiple of 15
The largest 4-digit number is 9999, divide 9999 by 15, get 666.6
So take the largesr integer less that that which is 666. Multiply
666 by 15 and get 9990, which is the largest 4-digit multiple of 15.
So the numbers we are looking for are these:
67x15, 68x15, ... , 666x15, inclusive
There's the same number of them as there are integers from 66 to 666
There are 666 integers from 1 to 666.
We need to subtract from that the number of integers from 1 to 66
666-66 = 600
So there are 600 4-digit multiples of 15.
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the product of two positive integers is 4028 and their gcf is 2.
4028 = 2x2014, the only factor of 2 (other than 1) is 2. So the
2 positive integers are 2 and 2014.
what is their lcm
Their lcm is 2014
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That's all for now. You are only allowed 2 questions and I answered 3.
Edwin
