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

Common Factors From Prime Factors

Find all the common factors of two numbers by spotting the subparts their prime factorisations share, then pick the biggest.

6 micro-lessons

Preview · progress not saved — Chapter 1 is free

Common Factors Are Shared Subparts

A common factor must be a subpart of BOTH factorisations.

The idea (Textbook p. 52)

Factors of 45 are subparts of $3 \times 3 \times 5$ . Factors of 75 are subparts of $3 \times 5 \times 5$ .

So a common factor must be a subpart of both.

1 / 2

Example 1: 45 and 75

Circling shared primes to find all common factors of 45 and 75.

Problem. Find the common factors and the HCF of 45 and 75. (Textbook p. 52, Example 1)

1 / 6

Examples 2 and 3 Solved

More common subparts, and a pair with none at all.

Problem. Find the common factors and HCF of 112 and 84, then of 96 and 275. (Textbook pp. 52–53)

1 / 5

Common Subparts Card

The three steps for common factors from prime factors.

Common factors from prime factorisations

1. Write both prime factorisations one above the other.

2. Circle matching primes, one from each row. Every circled group is a common factor.

3. Add 1. The biggest group is the HCF. If no prime matches, the HCF is 1.

Example:

3 \times 3 \times 5

and

3 \times 5 \times 5

share 3, 5 and 15, so the HCF of 45 and 75 is 15.

Common Factors of 50 and 60

Fill in the shared subparts step by step.

0 of 5 blanks filled

Figure it Out, Textbook p. 53 (a).

50 = 2 × 5 × 5 and 60 = 2 × 2 × × 5.

Shared primes: one and one .

Common factors: 1, 2, 5 and . HCF = .

Common Factors and HCF

Find the common factors and HCF of four pairs.

Find the common factors and the HCF

Figure it Out, Textbook p. 53. Find the common factors and the HCF of:

(b) 140, 275 (c) 77, 725 (d) 370, 592 (e) 81, 243

(b) 140 and 275*

Factorise both, circle the shared primes, list, pick the highest.

Same steps.

(d) 370 and 592*

Same steps.

(e) 81 and 243*

Same steps.

← previousEvery Factor From Prime Factors next →The HCF Shortcut

Common Factors Are Shared Subparts

A common factor must be a subpart of BOTH factorisations.

The idea (Textbook p. 52)

Factors of 45 are subparts of $3 \times 3 \times 5$ . Factors of 75 are subparts of $3 \times 5 \times 5$ .

So a common factor must be a subpart of both.

1 / 2