Edexcel IGCSE Math A 1.4.D Products of Prime Factors

Practise decomposing integers into prime factors and writing repeated primes with index notation.

Exam points

divide successively by prime numbers until every remaining factor is prime
group repeated prime factors and write them using positive integer powers
multiply the prime-power product to check it reproduces the original integer

[Maximum number: 4]

(a)

Write 720 as a product of its prime factors. Show your working clearly.

[ 3 ]

Example working:
$720=2\times360=2\times2\times180$
or
$720=3\times240=3\times3\times80$
Prime factors:
2, 2, 2, 2, 3, 3, 5

Final answer:
$2\times2\times2\times2\times3\times3\times5$
or
$2^4\times3^2\times5$

M1 for at least 2 correct stages. M1 for the full list of prime factors, condoning inclusion of 1. A1 dep on M2.

(b)

Find the smallest whole number that 720 can be multiplied by to give a square number.

[ 1 ]

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1.4.D Prime factor decomposition question 1

Question (a)

Question (b)