write the greatest four digit number which is divisible by 9. is it divisible by 3? what do you notice?
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write the greatest four digit number which is divisible by 9. is it divisible by 3? what do you notice?
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Step-by-step explanation:
First we need to find the LCM of 3, 6, and 9. I think it is easiest to get LCM by factoring the numbers.
3=3
6=2⋅3
9=32
Now we look at all the prime factors involved, then examine the greatest exponent for each.
The prime factors in those 3 numbers are 2 and 3.
For 2, there is only an exponent of 1.
For 3, the largest exponent is 2.
Therefore, the LCM is 2⋅32=18
We know the largest 4 digit number is 9999, let us see if that number is a multiple of 18.
9999÷18=555.5
Therefore, 9999 is not a multiple of 18. The greatest multiple of 18 below 9999 must be the 555th multiple. To find the value of that multiple, we just multiply.
555⋅18=9990
That is the number we are looking for. 9990 is the greatest 4 digit multiple of 3, 6, and 9.
Answer:
write the greatest four digit number which is divisible by 9. is it divisible by 3? what do you notice?