Lesson test: Primes and factorisation

Primes and factorisation

1.[1p]
How many positive divisors does $720 = 2^{4} \cdot 3^{2} \cdot 5$ have?

CorrectNot quite: 30

2.[2p]
Factorise $1800$ and $3150$ and use the standard forms to find $\gcd (1800, 3150)$ .

CorrectNot quite: 450

3.[2p]
Two positive integers have $\gcd (a, b) = 12$ and $lcm (a, b) = 360$ . If $a = 72$ , what is $b$ ?

CorrectNot quite: 60

4.[1p]
A sieve of Eratosthenes is run to find every prime up to $200$ . What is the largest prime whose multiples must be crossed out?

CorrectNot quite: 13

5.[2p]
By trial division, what is the smallest prime factor of $391$ ?

CorrectNot quite: 17

6.[2p]
The prime number theorem compares $π (x)$ with $\frac{x}{\ln x}$ . Evaluate $\frac{x}{\ln x}$ at $x = 100 000$ , rounded to the nearest whole number.

CorrectNot quite: 8686

7.[1p]
In the system $2 ℕ$ of even numbers, an element is "prime" if it is not a product of two even numbers. Which of these is not prime there?

$2$

The answer is: $12$

$6$

The answer is: $12$

$12$

Correct

$18$

The answer is: $12$

8.[2p]
Which of these numbers are prime?

Select all that apply

$91$

The answer is: $97$, $127$

$97$

Correct

$119$

The answer is: $97$, $127$

$127$

Correct

$143$

The answer is: $97$, $127$

9.[2p]
Given the standard forms of two numbers, match each quantity to how it is read off.

Greatest common divisor
Least common multiple
Number of divisors of one number

the product of each exponent plus one
the smaller exponent of each prime
the larger exponent of each prime

Show the answer

Greatest common divisor: the smaller exponent of each prime Least common multiple: the larger exponent of each prime Number of divisors of one number: the product of each exponent plus one

1.[1p] How many positive divisors does 720=24⋅32⋅5 have?

2.[2p] Factorise 1800 and 3150 and use the standard forms to find gcd(1800,3150).

3.[2p] Two positive integers have gcd(a,b)=12 and lcm(a,b)=360. If a=72, what is b?

4.[1p] A sieve of Eratosthenes is run to find every prime up to 200. What is the largest prime whose multiples must be crossed out?

5.[2p] By trial division, what is the smallest prime factor of 391?

6.[2p] The prime number theorem compares π(x) with xlnx. Evaluate xlnx at x=100000, rounded to the nearest whole number.

7.[1p] In the system 2ℕ of even numbers, an element is "prime" if it is not a product of two even numbers. Which of these is not prime there?

8.[2p] Which of these numbers are prime?

9.[2p] Given the standard forms of two numbers, match each quantity to how it is read off.

1.[1p]
How many positive divisors does $720 = 2^{4} \cdot 3^{2} \cdot 5$ have?

2.[2p]
Factorise $1800$ and $3150$ and use the standard forms to find $\gcd (1800, 3150)$ .

3.[2p]
Two positive integers have $\gcd (a, b) = 12$ and $lcm (a, b) = 360$ . If $a = 72$ , what is $b$ ?

4.[1p]
A sieve of Eratosthenes is run to find every prime up to $200$ . What is the largest prime whose multiples must be crossed out?

5.[2p]
By trial division, what is the smallest prime factor of $391$ ?

6.[2p]
The prime number theorem compares $π (x)$ with $\frac{x}{\ln x}$ . Evaluate $\frac{x}{\ln x}$ at $x = 100 000$ , rounded to the nearest whole number.

7.[1p]
In the system $2 ℕ$ of even numbers, an element is "prime" if it is not a product of two even numbers. Which of these is not prime there?

8.[2p]
Which of these numbers are prime?

9.[2p]
Given the standard forms of two numbers, match each quantity to how it is read off.