Factorizing a number to its prime Factors
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الشرح
👀 Let's look
Divisibility, G.C.F and L.C.M. Every whole number is a product of primes.
And that product is unique — there is only one way.
Prime and composite
A prime number is a whole number above 1 whose only factors are 1 and itself: 2, 3, 5, 7, 11, 13 and so on. Every other whole number above 1 is composite, which means it can be broken into smaller factors. 1 is neither.
Factorising a number into primes means writing it as a product of prime numbers only — carrying on until nothing left can be broken down any further.
The factor tree
Divide by the smallest prime that fits, write the two factors underneath, and repeat on any branch that is not prime yet. When every leaf is prime, the tree is finished.
It does not matter which factor you split first. Start 84 with 2 × 42 or with 4 × 21 and you still finish at 2² × 3 × 7. Every number has exactly one prime factorisation, and that is what makes it worth finding.
84
84 =2×42
42 =2×21
21 =3×7
Find any factor pair to start with.
أمثلة محلولة
Worked example84
Write 84 as a product of primes.
Worked example120
Write 120 as a product of primes.
Worked exampleA prime already
Factorise 47.