Prime Factors and Standard Form

IGCSE Edexcel Mathematics
1.4 Prime Factors
1.5 Standard Form
Key Concepts: Prime factorization uses only prime numbers. Highest common factor (HCF) is common primes with smallest powers. Lowest common multiple (LCM) uses all primes with greatest powers. Standard form is A × 10ⁿ with 1 ≤ A < 10.

Section A: Prime Factors

1. Write as a product of primes: [4]
(a) 84
(b) 180
(c) 315
(d) 512
2. Find the HCF and LCM of 60 and 96. [3]

Section B: Standard Form

3. Write in standard form: [3]
(a) 34,500
(b) 0.00072
(c) 5,960,000
4. Convert out of standard form: [3]
(a) 6.8 × 10³
(b) 4.2 × 10⁻⁴
(c) 9.01 × 10⁵

Section C: Applications

5. The mass of Earth is 5.97 × 10²⁴ kg. Write this as a normal number. [2]
6. Express 1.8 × 10⁵ divided by 6 × 10² in standard form. [2]
Total marks: 17

Mark Scheme

1. (a) 2 × 2 × 3 × 7 [1]; (b) 2² × 3² × 5 [1]; (c) 3² × 5 × 7 [1]; (d) 2⁹ [1]
2. HCF = 2³ × 3 = 24 [1]; LCM = 2⁵ × 3 × 5 = 480 [2]
3. (a) 3.45 × 10⁴ [1]; (b) 7.2 × 10⁻⁴ [1]; (c) 5.96 × 10⁶ [1]
4. (a) 6,800 [1]; (b) 0.00042 [1]; (c) 901,000 [1]
5. 5,970,000,000,000,000,000,000,000 kg [2]
6. (1.8/6) × 10^(5-2) = 0.3 × 10³ = 3.0 × 10² [2]