Multiples
A multiple is the ________________ of a whole number when multiplied by another whole number.
The lowest common multiple (LCM) is the lowest multiple that _______ or more numbers have in common.
product
two
A factor is one of the whole numbers you _______________ in a multiplication operation.
A ___________ __________ is a factor that two or more whole numbers have in common.
The greatest common factor (GCF) is the greatest whole number that divides into two or more other whole numbers with no ___________.
multiply
common factor
remainder
A prime number is a positive whole number greater than ___ that has only __ ______.
The factors of a prime number are ___ and _____.
A composite number is a positive whole number greater than 1 that has ______ ______ __ ______.
1, 2 factors
1, itself
more than 2 factors
BEDMAS stands for
Bonus: ____ ____ are also considered under the exponent category of BEDMAS.
Brackets, Exponents, Division, Multiplication, Addition, Subtracation
square roots
All numbers are divisible by this number
1
The one and two digit multiples of 5 are
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95
Draw a factor tree to find all the factors of 56.
Then use your factor tree to write 4 equations expressing 56 as a product of 2 of its factors.
1, 2, 4, 7, 8, 14, 28, 56
1 x 56 = 56
2 x 28 = 56
4 x 14 = 56
7 x 8 = 56
To determine the prime factorization of a muber you have to express the number as a ______ __ __ _____ _____.
product of its prime factors
Use order of operations to solve:
45 - 6 x 7 =
Show your work for each step.
45 - 42
= 3
If a number's last digit is a zero, you know it is divisible by at least 4 numbers from 1-12. What numbers are these?
1, 2, 5, 10
The one and two digit multiples of 8 are
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
Common factors of 12 and 16 are
1, 2, 4
Use prime factorization to find the GCF of 64 and 80.
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Prime factorization of 64 = 2⁶
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1
Prime factorization of 80 = 2⁴ × 5
Both 64 and 80 have prime factor of 2. The lowest exponent of 2 is 4. Therefore, the GCF of 64 and 80 is 24 = 16.
Use order of operations to solve:
144 / (9 - 3)2 =
Show your work for each step.
= 144 / 62
= 144 / 36
= 4
If the sum of the digits is divisible by these numbers*, the number is divisible by these numbers*.
*Numbers from 1-12
HINT: there are 2 numbers
3 and 9
The LCM of 75 and 250 is
750
The GCF of 15 and 90 is
15
Use prime factorization to find the LCM of 36 and 48.
36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
36 = 2² × 3²
48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
48 = 2⁴ × 3
2 → highest power is 2⁴
3 → highest power is 3²
Multiply:
LCM = 2⁴ × 3² = 16 × 9 = 144
Use order of operations to solve.
(5 + 7)2 / (14 - 6)
Show your work for each step.
(12)2 / 8
= 144 / 8
= 18
What is the divisibility rule for 11?
Alternate subtracting and adding the digits. If the number is 0 or a multiple of 11 it is divisible by 11.
The LCM of 80 and 120 is
1200
Use prime factorization to identify three common factors of 14 and 84
2, 7, 14
Find the GCF and LCM of 45 and 75 using prime factorization.
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
45 = 3² × 5
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
75 = 3 × 5²
Common prime factors: 3 and 5
Use the lowest powers: GCF=3×5=15
Use order of operations to solve:
[(10 - 4)2 - 4] / 2 =
Show your work for each step.
[(6)2 - 4] / 2
= [36 - 4] / 2
= 32 / 2
= 16
What numbers from 1-12 is 3,584 divisible by?
Test each number from 1 to 12 and provide a rationale for why 3,584 is or isn't divisible by that number.
1: Yes. Every number is divisible by 1.
2: Yes. 3,584 is even.
3: No. 3 + 5 + 8 + 4 = 20 → not divisible by 3.
4: Yes. Last 2 digits = 84 → divisible by 4.
5: No. Ends in 4, not 0 or 5.
6: No. Not divisible by 3 (fails 2 & 3 rule).
7 :Yes 3584 ÷ 7 = 512.
8:Yes. Last 3 digits = 584 → divisible by 8.
9: No. Digit sum is 20 → not divisible by 9.
10: No. Doesn’t end in 0.
11: No. Alternating sum: 3 - 5 + 8 - 4 = 2 → not divisible by 11.
12: No. Not divisible by 3 (fails 3 & 4 rule).