Back to Ganita Prakash: Class 7 Mathematics, Par...BackConcept

Every Factor From Prime Factors

Build every factor of a number from its prime factors, and learn how one counterexample can break a claim.

8 micro-lessons

Preview · progress not saved — Chapter 1 is free

Factors Are Subparts

Any group of primes taken from a factorisation multiplies to a factor.

Is 28 a factor of 840? (Textbook p. 50)

$840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7$ . Reorder the primes (that never changes a product):

$840 = (2 \times 2 \times 7) \times (2 \times 3 \times 5) = 28 \times 30$

1 / 3

Which Are Factors of 840?

Testing 14, 8 and 27 using prime subparts.

Problem. Using $840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7$ , decide whether 14, 8 and 27 are factors. (Textbook p. 51)

1 / 5

All the Factors of 225

Listing every factor by combining 1, 2, 3 and 4 primes.

Problem. Find all the factors of 225 using prime factorisation. (Textbook p. 51)

1 / 5

List All the Factors

Use prime factorisation to list every factor of five numbers.

List all the factors

Figure it Out, Textbook p. 51. List all the factors of:

(a) 90 (b) 105 (c) 132 (d) 360 (this number has 24 factors) (e) 840 (this number has 32 factors)

Start each one with its prime factorisation.

(a) 90 and (b) 105*

Prime factorisation first, then the subparts.

Prime factorisation first.

(d) 360 (24 factors)*

Count yours: are there 24?

(e) 840 (32 factors)*

Count yours: are there 32?

Factor or Not?

Decide using prime subparts, without dividing.

1 / 4

Is $2 \times 7$ a factor of $840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7$ ?

Claims That Need Checking

A conjecture is a claim not yet proved; one counterexample breaks it.

Anshu's claim (Textbook p. 51)

After looking at a few factorisations, Anshu says: "The larger a number is, the longer its prime factorisation will be."

1 / 3

Breaking Anshu's Claim

96 is smaller than 121 but has a longer factorisation.

Problem. Is Anshu's conjecture true? (Textbook pp. 51–52)

1 / 4

← previousPrime Factorisation next →Common Factors From Prime Factors

Factors Are Subparts

Any group of primes taken from a factorisation multiplies to a factor.

Is 28 a factor of 840? (Textbook p. 50)

$840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7$ . Reorder the primes (that never changes a product):

$840 = (2 \times 2 \times 7) \times (2 \times 3 \times 5) = 28 \times 30$

1 / 3

Which Are Factors of 840?

Testing 14, 8 and 27 using prime subparts.

Problem. Using $840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7$ , decide whether 14, 8 and 27 are factors. (Textbook p. 51)

1 / 5

Factor or Not?

Decide using prime subparts, without dividing.

1 / 4

Is $2 \times 7$ a factor of $840 = 2 \times 2 \times 2 \times 3 \times 5 \times 7$ ?