UNIT 1: FACTORS & EXPONENTS GREATEST COMMON FACTOR (GCF) LEAST COMMON MULTIPLE (LCM) EXPONENTS SQUARE ROOTS ORDER OF OPERATIONS

COMMON FACTORS METHOD #1 - USING A FACTOR TREE, FIND WHAT COMMON PRIME (ROOT) NUMBERS EACH HAS AND MULTIPLY THEM METHOD #2 - LIST THE FACTORS FOR EACH NUMBER - DETERMINE WHICH ARE COMMON - FIND THE LARGEST

COMMON FACTORS METHOD #1 - FIND THE GREATEST COMMON FACTOR (GCF) FOR THE NUMBERS 36 AND 48. 36 48 6 6 6 8 2 3 2 3 2 3 2 4 2 2 2 x 2 x 3 x 3 2 x 2 x 2 x 2 x 3 2 x 2 x 3 = 12

COMMON FACTORS 36 48 2 x 2 x 3 = 12 2 3 3 2 2 2

COMMON FACTORS METHOD #2 - LIST FACTORS 36 = 1 x 36 4 x 9 48 = 1 x 48 4 x 12 2 x 18 6 x 6 2 x 24 6 x 8 3 x 12 3 x 16 36 – (1, 2, 3, 4, 6, 9, 12, 18, 36) 48 – (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) - COMMON (1, 2, 3, 4, 6, 12) - GREATEST COMMON FACTOR (GCF) 12

COMMON MULTIPLES METHOD #1 - USING A FACTOR TREE, DETERMINE THE PRIME (ROOT) NUMBERS FOR EACH. - CREATE A VENN DIAGRAM (CIRCLES) AND MULTIPLY WHATEVER PRIME NUMBERS ARE IN THE CIRCLES METHOD #2 - LIST THE MULTIPLES OF EACH NUMBER - CIRCLE THE MATCHING NUMBERS - FIND THE LOWEST NUMBER

COMMON MULTIPLES METHOD #1 - FIND THE LEAST COMMON MULTIPLE (LCM) FOR THE NUMBERS 8 AND 12. 8 12 2 4 2 6 2 2 2 3 2 x 2 x 2 2 x 2 x 3 2 x 2 x 2 x 3 = 24

COMMON MULTIPLES 8 12 2 x 2 x 2 x 3 = 24 2 3 2 2

COMMON MULTIPLES METHOD #2 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104 12= 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 CIRCLE MATCHING 24, 48, 72 LEAST COMMON MULTIPLE (LCM) - 24

EXPONENTS We use powers to represent repeated multiplication 2 5 = 2 x 2 x 2 x 2 x 2 = 32 10 5 = 10 x 10 x 10 x 10 x 10 = 100000 10 𝑤𝑜𝑢𝑙𝑑 𝑏𝑒 𝑐𝑎𝑙𝑙𝑒𝑑 THE BASE 5 would be called 𝐓𝐇𝐄 𝐄𝐗𝐏𝐎𝐍𝐄𝐍𝐓

SQUARE ROOTS A square root is a product that when divided by a number we get the same number as an answer 25 = 25 ÷ 5 = 5 It is a perfect combination ie. 5 x 5 = 25

ORDER OF OPERATIONS BEDMAS Brackets Exponents (Square roots) Division & Multiplication Addition & Subtraction