Session 3: Digits, divisibility and logarithms

UCL Online STEP and AEA Preparation Sessions
Session 3: Digits, divisibility and logarithms
In this session you will look at how to deduce properties of a
number from its digits; how to spot factors of a numbers; the
usefulness of considering remainders to solve problems and
techniques involving logarithms, including how logs can help you
to find the first digit of a number.
You need to remember that the digits of a number are not the same
as the number itself.
The two-digit number whose digits are a then b which you would
write down as ‘ab’ is actually 10a + b. The three digit number ‘abc’
is actually 100a + 10a + b.
This technique enables you to answer question like
How many two digit numbers N have the property that the
sum of N and the number formed by reversing the digits of N
is a square?
The use of indices and logarithms will be considered.
How logarithms can be used to work out the first digit of 3100?
The session will also cover the technique of using remainders upon
division to solve problems, known as modular arithmetic.
The session will include discussion of associated examples from
STEP and AEA past papers.