USTET Mathematics — Arithmetic — Multiples, Factors, PEMDAS, Fractions & DecimalsFlash Cards

Find all factors of 24

Step 1: Start with 1 and 24 (always factors). Step 2: Check divisibility: 24÷2=12, 24÷3=8, 24÷4=6. Step 3: Stop when factors repeat. Answer: 1, 2, 3, 4, 6, 8, 12, 24

List the first 5 multiples of 8

Step 1: Multiply 8 by consecutive integers. Step 2: 8×1=8, 8×2=16, 8×3=24, 8×4=32, 8×5=40. Answer: 8, 16, 24, 32, 40

Determine if 117 is prime or composite

Step 1: Find √117 ≈ 10.8, so check primes up to 10. Step 2: Test divisibility by 2, 3, 5, 7. Step 3: 117÷3 = 39 (no remainder). Step 4: Since 117 is divisible by 3, it's composite. Answer: Composite (117 = 3 × 39)

Find the prime factorization of 60

Step 1: 60 = 2 × 30. Step 2: 30 = 2 × 15. Step 3: 15 = 3 × 5. Step 4: All factors (2, 2, 3, 5) are prime. Answer: 60 = 2² × 3 × 5

Find LCM of 12 and 18

Method 1: Prime factorization. 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 4 × 9 = 36. Method 2: List multiples. 12: 12, 24, 36... 18: 18, 36... Answer: LCM = 36

Find GCF of 24 and 36

Method 1: Prime factorization. 24 = 2³ × 3, 36 = 2² × 3². GCF = 2² × 3 = 12. Method 2: List factors. 24: 1,2,3,4,6,8,12,24. 36: 1,2,3,4,6,9,12,18,36. Answer: GCF = 12

Check if 2,346 is divisible by 3

Step 1: Add digits: 2 + 3 + 4 + 6 = 15. Step 2: Check if sum is divisible by 3: 15 ÷ 3 = 5. Step 3: Since 15 is divisible by 3, the original number is too. Answer: Yes, 2,346 is divisible by 3

Check if 1,248 is divisible by 4

Step 1: Look at last two digits: 48. Step 2: Check if 48 is divisible by 4: 48 ÷ 4 = 12. Step 3: Since 48 is divisible by 4, the entire number is. Answer: Yes, 1,248 is divisible by 4

Solve: 3 + 4 × 5 - 2

Step 1: Apply PEMDAS (multiplication before addition/subtraction). Step 2: 4 × 5 = 20. Step 3: 3 + 20 - 2. Step 4: Work left to right: 23 - 2 = 21. Answer: 21

Solve: (8 + 2) × 3² ÷ 5

Step 1: Parentheses first: (8 + 2) = 10. Step 2: Exponents: 3² = 9. Step 3: Multiplication/Division left to right: 10 × 9 = 90. Step 4: 90 ÷ 5 = 18. Answer: 18

Convert 3/4 to decimal

Step 1: Divide numerator by denominator. Step 2: 3 ÷ 4 = 0.75. Step 3: Check: 0.75 × 4 = 3 ✓. Answer: 0.75

Add: 2/5 + 1/3

Step 1: Find LCD of 5 and 3: LCD = 15. Step 2: Convert fractions: 2/5 = 6/15, 1/3 = 5/15. Step 3: Add: 6/15 + 5/15 = 11/15. Answer: 11/15

Multiply: 2/3 × 4/5

Step 1: Multiply numerators: 2 × 4 = 8. Step 2: Multiply denominators: 3 × 5 = 15. Step 3: Simplify if possible: 8/15 cannot be simplified. Answer: 8/15

Divide: 3/4 ÷ 2/3

Step 1: Change division to multiplication by reciprocal. Step 2: 3/4 × 3/2. Step 3: Multiply: (3×3)/(4×2) = 9/8. Step 4: Convert to mixed number: 9/8 = 1 1/8. Answer: 9/8 or 1 1/8

Add: 3.25 + 1.7

Step 1: Align decimal points. Step 2: Add zeros if needed: 3.25 + 1.70. Step 3: Add column by column: 5 + 0 = 5, 2 + 7 = 9, 3 + 1 = 4. Answer: 4.95

Multiply: 2.5 × 0.4

Step 1: Ignore decimals temporarily: 25 × 4 = 100. Step 2: Count total decimal places: 1 + 1 = 2. Step 3: Place decimal point: 1.00. Answer: 1.0 or 1

Convert 0.625 to fraction

Step 1: Write as fraction: 625/1000. Step 2: Find GCF of 625 and 1000: GCF = 125. Step 3: Divide both by GCF: 625÷125 = 5, 1000÷125 = 8. Answer: 5/8

When do you use prime factorization to find LCM?

Use when: 1) Numbers are large (harder to list multiples), 2) Finding LCM of 3+ numbers, 3) Need to show work systematically. Method: Factor each number, then take highest power of each prime. Example: LCM(12,18) = 2²×3² = 36

What's the difference between factors and multiples of 6?

Factors divide INTO 6: 1, 2, 3, 6 (finite list, ≤ 6). Multiples are 6 times other numbers: 6, 12, 18, 24... (infinite list, ≥ 6). Memory tip: Factors are Few and small, Multiples are Many and large.

Why does the divisibility rule for 9 work?

Because 10 ≡ 1 (mod 9), 100 ≡ 1 (mod 9), etc. So any number abc = 100a + 10b + c ≡ a + b + c (mod 9). If digit sum is divisible by 9, so is the original number. Example: 729 → 7+2+9=18 → 1+8=9, divisible by 9.