Download `a` is divisible by another number

MATHS 2
ND
IES MACARENA
ESO – WORKSHEET 3
DIVISIBILITY
MULTIPLES AND DIVISORS
A number ‘a’ is divisible by another number ‘b’ if after dividing the remainder is zero. In this
case ‘a’ is multiple of ‘b’ and ‘b’ is a divisor of ‘a’.
A prime number is a number that has only two divisors: the number itself and 1.
Exercises:
1. Find out three multiples and all the divisors of the next numbers:
a) 12
b) 11
c) 6
d) 9
How many multiples does any integer have?
2. Which of the following numbers are prime numbers?
3, 6, 7, 8, 16, 17 and 23
DIVISIBILITY RULES CHART
A number is divisible by …
2 if the last digit is even (0, 2, 4, 6 or 8)
3 if the sum of the digits is divisible by 3
4 if the last two digits form a number divisible by 4
5 if the last digit is 0 or 5
6 if the number is divisible by both 2 and 3
9 if the sum of the digits is divisible by 9
10 if the last digit is 0
11 if the result of the next operation is 0 or divisible by
11: subtract the addition of all the even-numbered digits
from the addition of all the odd-numbered digits.
Divisible
3,978
Not divisible
4,975
315
139
8,512
7,518
14,975
10,978
48
711
20
93
15,990
10,536
2541
2542
3. Check the divisibility of the number 840,114 by: 2, 3, 5, 10 and 11.
PRIME FACTORIZATION
Every positive integer greater than 1 can be written in only one way as a product of prime
number powers. For example:
90 = 2 · 32 · 5
4. Find the prime factorization of the next numbers:
a) 60
b) 180
c) 132
d) 441
THE GREATEST COMMON DIVISOR
The Greatest Common Divisor (GCD) of two numbers is the biggest number that is a divisor
of both numbers. For example:
- The divisors of 12 are 1, 2, 3, 4, 6 and 12.
- The divisors of 20 are 1, 2, 4, 5, 10 and 20.
- The common divisors of 12 and 20 are 1, 2 and 4, so the GCD of both numbers is 4.
5. Find out the GCD of the following pairs:
a) 72 y 108
b) 60 y 90
c) 21 y 45
d) 28 y 50
THE LEAST COMMON MULTIPLE
The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple
of both numbers. For example:
- The multiples of 12 are 12, 24, 36, 48, 60, 72, etc.
- The multiples of 20 are 20, 40, 60, 80, 100, etc.
- The common multiples are 60, 120, 180, etc., so the LCM of both numbers is 60.
6. Find out the LCM of the following pairs:
a) 72 y 108
b) 60 y 90
c) 21 y 45
7. Find out the multiples of 7 between 20 and 40.
8. Find out the divisors of 1080
9. Find out the prime numbers between 100 and 110.
10. Find out the GCD and the LCM of 24, 54 and 36.
d) 28 y 50