Which one is prime number?

Question

a. 5! + 7!
b. 3^7 - 1
c. 2^7 - 1
d. 54321
e. 12357

can you please explain how you found the answer (without calculator?)

Thank you

Answer 1

The sum of the digits in d. and e. are both divisible by 3 (5+4+3+2+1 = 15, 1+2+3+5+7 = 18), so neither d nor e can be prime.

3^7 - 1 ends up being an even number (since multiplying 3 by itself any number of times gives you an odd number, and then subtracting 1 makes it even), so it can not be prime.

All factorials are even numbers, so the sum of 2 factorials can not be a prime number.

As a result, the answer is c.) by process of elimination.

Answer 2

Here goes!
a. 5!/7! = 1/(7x6) which is not a prime #
b. 3^n results in an uneven number and
when you subtract 1 and it becomes
even and divisible by 2
d. The old rule, 5+4+3+2+1 = 15
then 54321 should be divisible by 3 or 5
trying 3, you get 18107 and therefore
54321 is not prime
e. 1+2+3+5+7 = 18
factors may be 2,3,6,9
trying 3, gives you 4119
therefore 12357 is not prime
c. We are left with 2^7-1 or 127
This is your prime number

Answer 3

Toss out the easiest ones first...
(a) If I add two factorials they are both even numbers so is their sum,
(d) ends in 21 and is divisible by 3.
(e) Adding the digits 1+2+3+5+7=18, so it's divisible by 9

The 2 remaining are plug and chug... use little chunks:

B) 3 cubed squared x 3, less 1 = (27x27x3) - 1=
Don't multiply, just look... X7xX7=XX9, XX9x3= XX7
If I subtract one, the answer (whatever it is!) is EVEN.

SO THE ANSWER IS (C):
2 cubed squared x 2 less 1 = (8x8x2) - 1 =127

Answer 4

Let's take the numbers one at a time:
a. 5! + 7! = 5!(1+ 6*7) since 7! = 7*6*5!
so a. is composite.
b. 3^7 - 1 is even, so it is composite.
d. 54321. The digits of this number add to 15, which
is a mulitple of 3, so d. is composite.
e. 12357. Same as d. Here the digits add to 18.
That leaves c. 2^7-1 = 127.
The integer part of the square root of this number is 11.
So we must see if 127 is divisible by 2,3,5,7 or 11.
Since none of these divide 127, 127 is prime.
The answer is c.

Answer 5

A: Both 5! and 7! are divisible by 5!
B: 3^7 is odd, so...
C: Might be prime
D: Look at the sum of the digits
E: Look at the sum of the digits

Answer 6

probably "C" because ....

d & e.) the sum of the digits of either number is divisible by 3. This is characteristic of any number divisible by 3.

b.) 3^7 is divisible by 3. Any number divisible by 3, minus 1, is divisible by 2 or 5.

a.)5! + 7! = 5!(1 + 6*7); this makes the number divisible by 5!

Answer 7

Answer: c. 2^7 - 1 is equal to (128 - 1) or 127. 127 is a prime number. I did it without using even pen and paper to figure out the outcome of multiplying 2 seven times by itself. You can easily do it I know.

Answer 8

c. 2^7 - 1

Answer 9

42

Answer 10

choice c is the answer