Question

Q1 which of the following is a factor of 1x2x3x.....x35x36

a)37 b)53 c)62 d)82

Q2) If the sum of 2016 different whole numbers is odd. at most how many of the numbers can be even

a)0 b)1 c)2014 d)2015

Answer 1

Hellllooooooo is C)2014 kkk

Answer 2

• Q1: c) 62
• Q2: d) 2015

Explanation:

Q1

It pays to know divisibility rules and multiplication tables. If you do, you know that 37 and 53 are prime numbers (have no factors other than themselves and 1) and that 62 and 82 are divisible by 2:

• 62 = 2 × 31 . . . . where 31 is prime
• 82 = 2 × 41 . . . . where 41 is prime

The only one of any of these numbers that has factors all less than 36 is 62. So 62 is a factor of ... 1 × 2 × 3 ... × 30 × 31 × 32 ... ×36

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Q2

For the sum to be odd, there must be an odd number of odd numbers in it. The least number of odd numbers required is 1, so there can be up to 2015 even numbers.