Sec 1 Mathematics Primes, HCF & LCM topical questions

List all the factors of 36, then state which of them are prime.

Express 45 as a product of prime factors.

Find the HCF and the LCM of 12 and 18.

Evaluate 14² and the cube root of 343.

Evaluate 3⁴ − 5².

Find the HCF and the LCM of 26 and 39.

Two numbers are A = 180 and B = 168.

1. (a)Express A and B each as a product of prime factors in index notation.[2]
2. (b)Hence find the HCF of A and B.[1]
3. (c)Hence find the LCM of A and B.[1]

A clock chime plays every 8 minutes and a gong sounds every 12 minutes. Both sound together at 07:00. Find the next time they sound together.

A square garden has an area of 196 m². Find the perimeter of the garden.

A hawker stall prepares 60 otah-otah and 84 curry puffs for identical festive sets, with no food left over.

1. (a)Find the greatest number of identical sets the stall can prepare.[2]
2. (b)State how many otah-otah and how many curry puffs go into each set.[2]

At an MRT platform, a northbound train departs every 9 minutes and an eastbound train every 15 minutes. Both depart at 07:12. Find the next time both depart together.

N = 2³ × 3² × 5. Find the smallest positive integer k such that N × k is a perfect square.

The HCF of two numbers, each between 10 and 40, is 6 and their LCM is 36. One of the numbers is 12. Find the other number.

Three strips of ribbon measure 72 cm, 120 cm and 156 cm. They are each cut into equal pieces of the greatest possible length, with no ribbon wasted.

1. (a)Find the greatest possible piece length.[2]
2. (b)Find the total number of pieces.[2]

A rectangular HDB corridor floor measures 360 cm by 480 cm. It is covered exactly, with no cutting, by the largest possible identical square tiles.

1. (a)Find the side length of the largest square tile that works.[2]
2. (b)Find the total number of tiles used.[2]