Number Play MATHS - Number Play

Make conjectures by examining if there are any patterns or relations between
(i) the parity of a number and its digital root.
(ii) the digital root of a number and the remainder obtained when the number is divided by 3 or 9.

What will be the digital root of the number 9a + 36b + 13?

Write any number. Generate a sequence of numbers by repeatedly adding 11. What would be the digital roots of this sequence of numbers? Share your observations.

The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?

How many multiples of 9 are there between the numbers 4300 and 4400?

Choose any 3 numbers. When is their sum divisible by 3? Explore all possible cases and generalise.

Write five multiples of 36 between 45,000 and 47,000. Share your approach with the class.

If 3p7q8 is divisible by 44, list all possible pairs of values for p and q.

Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5. What is the smallest such number? Can you give a simple explanation of why it is the smallest?

Which of the following Venn diagrams captures the relationship between the multiples of 4, 8, and 32?

Is the product of two consecutive integers always multiple of 2? Why? What about the product of these consecutive integers? Is it always a multiple of 6? Why or why not? What can you say about the product of 4 consecutive integers? What about the product of five consecutive integers?

Deepak claims, “There are some multiples of 11 which, when doubled, are still multiples of 11. But other multiples of 11 don’t remain multiples of 11 when doubled”. Examine if his conjecture is true; explain your conclusion.

Find three consecutive numbers such that the first number is a multiple of 2, the second number is a multiple of 3, and the third number is a multiple of 4.
Are there more such numbers? How often do they occur?

Suppose p is the greatest of five consecutive numbers. Describe the other four numbers in terms of p.

Write a 6-digit number that it is divisible by 15, such that when the digits are reversed, it is divisible by 6.

The middle number in the sequence of 5 consecutive even numbers is 5p. Express the other four numbers in sequence in terms of p.

Sreelatha says, "I have a number that is divisible by 9. If I reverse its digits, it will still be divisible by 9 ".
(i) Examine if her conjecture is true for any multiple of 9.
(ii) Are any other digit shuffles possible such that the number formed is still a multiple of 9 ?