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Factors, Multiples, Primes
•Use simple tests of divisibility.•Recognise multiples.•Recognise primes (less than 100).•Recognise lowest common multiples.•Recognise highest common factors.•Write a number as a product of its prime factors.
Multiples, Factors andPrimes
What are the first five multiples of:a) 3b) 4c) 11d) 21
3, 6, 9, 12, 154, 8, 12, 16, 2011, 22, 33, 44, 5521, 42, 63, 84, 105
A multiple of a number is what you get when you multiply that number by some other whole number.
Multiples are Usually Larger Than Individual numbers, Possibly Larger never Ever Smaller
Factors, Multiples, Primes
• http://www.visnos.com/demos/sieve-of-eratosthenes
Factors, Multiples, Primes
7
11 19
23
2
17
3749
9
2245
63 57 81
27
69
77 99
1
X 7 23
17
11 19
X
X 2
X XX X XX X X
X X 37
39
Identify the prime numbers in the grid below. There are 7 to find.
Factors, Multiples, Primes
Lowest Common Multiple – the lowest number in two or more numbers’ times tables.
Q. Find the LCM of 4 and 6.1. Write out the first six numbers the 4 and 6
times tables2. Look for the first number that appears in
both lists.
Factors, Multiples, Primes.
• https://www.youtube.com/watch?v=GKTexzwFpck
Factors, Multiples, Primes
Example LCMQ. Find the LCM of 4 and 6
4 4, 8, 12, 16, 20, 24,….
6 6, 12, 18, 24, 30, 36,…
We want the LOWEST common multiple, so the LCM of 4 and 6 is… 12
Factors, Multiples, Primes
a) 2 and 5
b) 3 and 4
c) 4 and 8
d) 5 and 6
e) 3 and 8
f) 4 and 9
g) 8 and 10
h) 4, 5 and 12.
10
12
8
30
24
36
40
60
Find the LCM of the following:
Factors, Multiples, Primes
What are the factors of:a) 16b) 30c) 8d) 7
1, 2, 4, 8, 161, 2, 3, 5, 6, 10, 15, 301, 2, 4, 81, 7
A factor is a whole number which divides exactly into a whole number, leaving no remainder.
Factors Are Certainly Tiny Or Really SmallA prime number has exactly two factors:
1, and the number itself.
Factors, Multiples, Primes
Prime Factors• We can use a ‘factor tree’ to enable us to
write a number as “a product of its prime factors”
• Each time you reach a prime number, you stop and circle that number.
Factors, Multiples, Primes
• Example: Write 84 as a product of its prime factors
• 84 = 2 x 2 x 3 x 7• 84 = 22 x 3 x 7
• Now your turn: Write 42 as a product of prime factors.
84
2 42
2 21
3 7
Factors, Multiples, Primes
• Highest Common Factor (HCF) – the LARGEST number that goes into two or more numbers exactly.
• Write out all the factors for each number….
• Example: Find the HCF of 32 and 5632 1, 2, 4, 8, 16, 3256 1, 2, 4, 7, 8, 14, 28, 56 HCF = 8
Factors, Multiples, Primes
a) 8 and 12
b) 9 and 15
c) 10 and 30
d) 18 and 33
e) 32 and 80
f) 60 and 108
g) 36, 64, and 76
h) 48, 60 and 84
Find the HCF of the following numbers:
4
3
10
3
16
12
4
12
Factors, Multiples, Primes
Your turn…1. Find the HCF of the
following:
a) 18 and 28b) 16 and 40c) 42 and 90d) 40 and 63e) 20, 64 and 108f) 54, 90 and 162
2. Find the LCM of the following:
a) 4 and 5b) 8 and 12c) 6 and 9d) 12 and 15e) 5, 8 and 10f) 4, 7 and 9
3. Write the following as products of their prime factors.
a) 18 b) 135 c) 154 d) 2310
2861
418
2024186040252
32 x 2 33 x 5 2 x 7 x 11 2 x 3 x 5 x 7 x 11
•Use simple tests of divisibility.•Recognise multiples.•Recognise primes (less than 100).•Recognise lowest common multiples.•Recognise highest common factors.•Write a number as a product of its prime factors.
Factors, Multiples, Primes
HCF and LCM
• Calculate the HCF and LCM of 48 and 6048 60
48 = 2 x 2 x 2 x 2 x 3
48 = 2 x 2 x 2 x 2 x 360 = 2 x 2 x 3 x 5
48 60
22
22
332 2
5
• Multiply the numbers in the overlap to get the HCF• Multiply all the numbers in the Venn diagram to get the LCM.
HCF = 2 x 2 x 3 = 12LCM = 2 x 2 x 3 x 2 x 2 x 5 = 240
Find the HCF and LCM of the following:
24 and 30
36 and 50
16 and 72
