012e. Divisibility Rules and Division Vocabulary

Learning Intentions

To know the meaning of the terms divisible, divisor, dividend, quotient and remainder
To understand that divisibility tests can be used to check if a number is divisible by another number without performing the division
test for divisibility by 2, 3, 4, 5, 6, 8, 9 and 10

Identify division vocabulary using $23 \div 5 = 4$ remainder $3$ :
a) Dividend
b) Divisor
c) Quotient
d) Remainder

Use divisibility tests:

a) Is $248$ divisible by $2$ ?
b) Is $375$ divisible by $5$ ?
c) Is $4 560$ divisible by $10$ ?

Use divisibility tests:

a) Is $432$ divisible by $3$ ?
b) Is $5 148$ divisible by $9$ ?
c) Is $624$ divisible by $4$ ?

Use divisibility tests:

a) Is $1 236$ divisible by $6$ ?
b) Is $3 216$ divisible by $8$ ?
c) Is $2 970$ divisible by $3$ and $5$ ?

Using $19 \div 4 = 4$ remainder $3$ , identify:
a) Dividend
b) Divisor
c) Quotient
d) Remainder

Use divisibility tests:

a) Is $346$ divisible by $2$ ?
b) Is $845$ divisible by $5$ ?
c) Is $7 820$ divisible by $10$ ?

Use divisibility tests:

a) Is $528$ divisible by $3$ ?
b) Is $6 345$ divisible by $9$ ?
c) Is $732$ divisible by $4$ ?

Use divisibility tests:

a) Is $2 412$ divisible by $6$ ?
b) Is $4 128$ divisible by $8$ ?
c) Is $5 940$ divisible by $3$ and $5$ ?

Identify the terms in $27 \div 6 = 4$ remainder $3$ :
a) Dividend
b) Divisor
c) Quotient
d) Remainder
Test divisibility by $2$ , $5$ and $10$ :
a) $468$
b) $735$
c) $9 240$
Test divisibility by $3$ and $9$ :
a) $324$
b) $5 436$
c) $7 812$
Test divisibility by $4$ and $8$ :
a) $316$
b) $2 448$
c) $6 432$
Test divisibility by $6$ :
a) $342$
b) $1 248$
c) $4 530$
Determine all numbers each is divisible by from $2, 3, 4, 5, 6, 8, 9, 10$ :
a) $720$
b) $3 456$
c) $5 940$

Explain why a number divisible by $10$ must also be divisible by $2$ and $5$ .
Why must a number divisible by $6$ also be divisible by $2$ and $3$ ?
A student says $4 512$ is divisible by $4$ because $4 + 5 + 1 + 2 = 12$ . Explain the mistake.
Explain why divisibility tests are useful.

Find all numbers between $40$ and $60$ divisible by $3$ .
A number is divisible by $5$ and $9$ . It is less than $100$ . What could the number be?
Which numbers between $200$ and $230$ are divisible by $4$ ?
A number is divisible by $2$ , $3$ , and $5$ . It is less than $200$ . Give two examples.
Find a number greater than $500$ that is divisible by $8$ and $10$ .

Students may confuse divisor and dividend
Students may believe divisibility tests give the quotient rather than just checking divisibility
Students may incorrectly add digits for divisibility by $4$ or $8$
Students may forget that divisibility by $6$ requires divisibility by both $2$ and $3$
Students may think numbers ending in $0$ are only divisible by $10$
Students may misapply divisibility rules to the entire number instead of the last digits where required