Question

Help me me me me me me

Answer 1

A) 312

B) 156

C) 234

D) 78

E) 390

Explanation:

In number theory, the prime factors of an integer are the prime numbers that are exact divisors of that integer.

To find out if 13 is a divisor of the numbers shown, you must divide each number by 13, and if in the end the result is an integer (which means that the remainder of the division is 0), then it is a prime factor of that number.

• A) 312 ÷ 13 = 24 (13 IS a prime factor of 312)
• B) 598 ÷ 13 = 46 (13 IS a prime factor of 46)
• C) 234 ÷ 13 = 18 (13 IS a prime factor of 234)
• D) 78 ÷ 13 = 6 (13 IS a prime factor of 78)
• E) 390 ÷ 13 = 30 (13 IS a prime factor of 390)
• F) 156 ÷ 13 = 12 (13 IS a prime factor of 156)
• G) 897 ÷ 13 = 69 (13 IS a prime factor of 897)
• H) 138 ÷ 13 = 10.615384615384615 (13 IS NOT a prime factor of 138)

So, until now, the numbers that can be selected are:

• A) 312
• B) 598
• C) 234
• D) 78
• E) 390
• F) 156
• G) 897

For the other numbers (2 and 3), you can apply the same method, but there are "tricks" to make it faster:

If the number has the number 2 as a prime factor, it must end in an even number or 0

• A) 312 ends with a even number (2) 2 IS a prime factor of 312)
• B) 598 ends with a even number (8) 2 IS a prime factor of 156)
• C) 234 ends with a even number (4) 2 IS a prime factor of 234)
• D) 78 ends with a even number (8) 2 IS a prime factor of 78)
• E) 390 ends with Zero 2 IS a prime factor of 390
• F) 156 ends with a even number (6) 2 IS a prime factor of 156)
• G) 897 ends with a even number (7) 2 IS NOT a prime factor of 897)

Now, the numbers that can be selected are:

• A) 312
• B) 598
• C) 234
• D) 78
• E) 390
• F) 156

If the number has the number 3 as a prime factor, the sum of all its terms is a multiple of 3.

• A) 312: 3 + 1 + 2 = 6

"6" is a multiple of 3, therefore 312 DOES HAVE 3 as a prime factor

• B) 598 : 5 + 9 + 8 = 22 = 2 + 2 = 4

"4" is NOT a multiple of 3, therefore 598 DOES NOT HAVE 3 as a prime factor

• C) 234: 2 + 3 + 4 = 9

"9" is a multiple of 3, therefore 234 DOES HAVE 3 as a prime factor

• D) 78: 7 + 8 = 15 = 1 + 5 = 6

"6" is a multiple of 3, therefore 78 DOES HAVE 3 as a prime factor

• E) 390: 3 + 9 + 0 = 12 = 1 + 2 = 3

"3" is a multiple of 3, therefore 390 DOES HAVE 3 as a prime factor

• F) 156: 1 + 5 + 6 = 12 = 1 + 2 = 3

"3" is a multiple of 3, therefore 156 DOES HAVE 3 as a prime factor

• H) 138: 1 + 3 + 8 = 12 = 1 + 2 = 3

"3" is a multiple of 3, therefore 138 DOES HAVE 3 as a prime factor

Finally, the numbers that can be selected are:

• A) 312
• C) 234
• D) 78
• E) 390
• F) 156