Factors, Multiples & Primes

How is a factor defined in mathematics?

A whole number that divides into another number with no remainder.

What criteria must a number meet to be classified as a prime number?

A whole number greater than 1 with exactly two factors: 1 and itself (e.g., 2, 3, 5, 7, 11, 13, 17, 19, 23, 29).

Why is the number 1 explicitly excluded from being a prime number?

Because it only has one factor (itself), whereas prime numbers must have exactly two factors.

What does it mean to express a number as a product of prime factors?

Expressing a composite number as prime numbers multiplied together (usually written in index form).

How would you write 180 as a product of prime factors in index form?

2² × 3² × 5 (found using a factor tree).

How do you define the Highest Common Factor (HCF) of two numbers?

The largest whole number that divides exactly into two or more target numbers.

What is meant by the Lowest Common Multiple (LCM) of a set of numbers?

The smallest whole number that is a multiple of two or more target numbers.

How do you calculate the HCF of two numbers using their prime factors in a Venn diagram?

Multiply ONLY the prime factors located in the center overlapping section.

How do you calculate the LCM of two numbers using their prime factors in a Venn diagram?

Multiply ALL the prime factors across the ENTIRE Venn diagram.

What are the HCF and LCM of 60 and 72?

HCF = 12, LCM = 360. (Prime factors: 60 = 2² × 3 × 5, 72 = 2³ × 3². Center intersection = 2 × 2 × 3).