M.Mar Agüera de Pablo-Blanco
IES Caura. Coria del Río
Bilingual programme
UNIT 5. MULTIPLES AND FACTORS.
PRIME NUMBERS. LOWEST COMMON
MULTIPLE AND HIGHEST COMMON
FACTOR.
 You must know what a multiple and a factor are.

A multiple is a number in the times table.
You can find them multiplying the number by 1, 2, 3, 4, 5,......
EXAMPLE: The multiples of 4 are:
4,8,12,16,20,24,…….
EXERCISE:
The
multiples
of 7 are:

A factor is a number that divides into another number exactly. I
mean, when the division is an exact division.
Remember, in a division: D
r
d
q
These terms are called:
D= dividend
d=divisor
q=quotient
r=remainder
Remember the rule in a division:
D  d q  r
When the remainder is 0 (r=0), the division is called
Exact division.
And now
EXAMPLE:
The factors of 20 are: 1,2,4,5,10,20.
(All these numbers divide into 20 exactly).
EXERCISE:
The
factors of
80 are:
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M.Mar Agüera de Pablo-Blanco
IES Caura. Coria del Río
Bilingual programme
 You must know what a prime number is.

A prime number is a number with only two factors, itself
and 1.

A composite number is a number with more than two
factors.

To find prime numbers, you can use the following tests of
divisibility:
A number is divisible by:




EXERCISE:

2 if the last digit is 0,2,4,6 or 8.
3 if the sum of the digits is a number on the 3 times
table.
5 if the last digit is 0 or 5.
11 if the sum of every digit which is in odd place
minus the sum of the digits in even place is equal to 0
or 11.
Find the prime numbers up to 50 are:
FACTORISATION: To factorise a composite number is to
write it as a
product of prime factors.
EXAMPLE:
Divide the number by
the first prime numbers
2,3,5,7,11,13,………,
and look for factors.
20
10
5



2
2
5

20  2  2  5 1
1
2
M.Mar Agüera de Pablo-Blanco
IES Caura. Coria del Río
Bilingual programme
EXERCISE:
Write as a product
of prime factors
the number 50
50
 You must know what the lowest common multiple and
the highest common factor are.
 Abbreviations:
ENGLISH
SPANISH
lowest common
multiple
LCM
mínimo común
múltiplo
highest common
factor
HCF máximo común divisor
mcm
mcd
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M.Mar Agüera de Pablo-Blanco
IES Caura. Coria del Río
Bilingual programme
EXAMPLE:
STEP 1
STEP 2
STEP 3
Find the HCF of 640 and 192:
Write the
84  2
numbers as 42  2
the products 21  3
of their
7  7
prime
1
factors.
Ring the
factors in
common
Multiply all
these
factors in
common
EXERCISE:
360
180
90
45
15
5
1






2
2
2
3
3
5
360  2  2  2  3  3  5 1
84  2  2  3  7  1
360  2  2  2  3  3  5 1
84  2  2  3  7  1
2  2  3 1  12
The HCF is 12
Find the HCF of 250 and 115:
STEP 1
STEP 2
STEP 3
The HCF is 5
4
M.Mar Agüera de Pablo-Blanco
IES Caura. Coria del Río
Bilingual programme
EXAMPLE:
Find the LCM of 640 and 192:
STEP 1 Divide and look for
the prime factors
STEP 2 Write both numbers
as a product of their
prime factors.
STEP 3 Write in index form
and ring all the
factors with the
highest index.
640
320
160
80
40
20
10
5
1








192  2
96  2
48  2
24  2
12  2
6  2
3  3
1
2
2
2
2
2
2
2
5
640  2  2  2  2  2  2  2  5 1
192  2  2  2  2  2  2  3 1
640  2 7  5  1
192  2 6  3  1
2 7  3  5  1  1920
STEP 4 Multiply all these
factors.
EXERCISE:
The answer is 1920
Find the LCM of 49 and 77:
STEP 1
STEP 2
STEP 3
STEP 4
The answer is 539
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