True or false?

In your book, Maths Mela (Chapter 13, Animal Jumps), Question 8 gives statements about factors and multiples and asks: true or false? To decide, test each statement with a few numbers. One example that breaks a statement is enough to show it is false.

'Factors of even numbers must be even.' Test 6: its factors are 1, 2, 3 and 6. 1 and 3 are odd! So this is false. 'Multiples of odd numbers cannot be even.' Test 3: 3 × 2 = 6, and 6 is even. So this is false too.

'Factors of odd numbers cannot be even.' Test 15: its factors are 1, 3, 5 and 15, all odd. It is always so, because an even number times any number gives an even answer, never an odd one. So this is true.

Numbers that come one after the other, like 4 and 5 or 8 and 9, are called consecutive numbers. 'One of the common multiples of two consecutive numbers is their product.' 4 × 5 = 20, and 20 is in both the 4 and the 5 times tables. True. 'The only common factor of two consecutive numbers is 1.' The factors of 8 are 1, 2, 4, 8 and of 9 are 1, 3, 9: only 1 is shared. True.