Number of Factors of a Natural Number
How many positive factors does 7 have?
2: 1 and 7.
Find the GCF of 6 and 9.
3.
What is the GCF of two relatively prime numbers?
1.
Find the LCM of 3 and 4.
12.
What are the prime factors of 10?
2 and 5.
List all the positive factors of 12. How many are there?
6 factors: 1, 2, 3, 4, 6, 12.
Find the GCF of 18 and 24.
6.
Are 8 and 15 relatively prime? Explain.
Yes. Their only common positive factor is 1.
Find the LCM of 6 and 8.
24.
Write 24 as a product of prime factors.
2³ × 3.
How many positive factors does 36 have?
9. Since 36 = 2² × 3², the number of factors is (2 + 1)(2 + 1) = 9.
Find the GCF of 36, 48 and 60.
12.
Which numbers are relatively prime to 18: 10, 25, 27 and 35?
25 and 35.
Each has a GCF of 1 with 18.
Find the LCM of 6, 10 and 15.
30.
Write 90 as a product of prime factors.
2 × 3² × 5.
A number has prime factorization 2³ × 5². How many positive factors does it have?
12: (3 + 1)(2 + 1) = 12.
Find the GCF of A = 2³ × 3² × 5 and B = 2² × 3 × 7.
12: 2² × 3.
A pupil says, “Two composite numbers cannot be relatively prime.” Is this true? Give a counterexample.
False. For example, 9 and 10 are composite, but their GCF is 1
One bus leaves every 12 minutes. Another leaves every 18 minutes. They leave together at 09:00. When is their next joint departure?
09:36.
LCM(12, 18) = 36 minutes.
Find the missing exponent: 360 = 2ᵃ × 3² × 5.
a = 3,
because 360 = 2³ × 3² × 5.
Find the smallest natural number that has exactly 6 positive factors.
12. Its factors are 1, 2, 3, 4, 6, 12.
A teacher has 48 pencils and 72 erasers. She makes the greatest possible number of identical gift bags, using every item. How many bags can she make, and what is in each bag?
24 bags, each containing 2 pencils and 3 erasers
Find all natural numbers less than 15 that are relatively prime to 15
1, 2, 4, 7, 8, 11, 13 and 14
Two natural numbers have a GCF of 6 and an LCM of 72. One number is 18. Find the other number.
24.
The other number is (6 × 72) ÷ 18 = 24.
A number has exactly three prime factors: 2, 3 and 5. It is divisible by 8 and 9. Find the smallest possible number.
360
2³ × 3² × 5