Divisibility
Is 84 divisible by 2, 3, and 6?
Even (✔2); 8+4=12 divisible by 3 (✔3); divisible by 6 iff by 2 and 3 → ✔6.
Answer: Yes to all.
Find the GCD of 18 and 24.
GCD(18, 24) = 6.
Write ¾ as a decimal and as a percentage.
3/4 = 0.75 = 75%
Express 4,500,000 in scientific notation
4,500,000 = 4.5 × 106.
Write 25% as a fraction and check if 250 is divisible by 5.
25% = 1/4; 250 ÷ 5 = 50 → divisible by 5 (✔)
Check divisibility of 945 by 3 and 9.
945 with 3 and 9 → 9+4+5=18, multiple of 3 and 9 → ✔ both.
Find the GCD of 340 and 213
GCD(340, 213) = 1 (coprime)
Write 0.875 as a fraction and percentage
0.875 = 7/8 = 87.5%
Express 0.00047 in scientific notation
0.00047 = 4.7 × 10-4
Write 0.25 as a fraction and check if 250 is divisible by 6
0.25 = 1/4; 250 is not divisible by 6 (not divisible by 3)
Find all divisors of 60
Divisors of 60 → {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}
Find the GCD of 84, 132, and 228
GCD(84, 132, 228) = 12
Write 125% as a decimal and a fraction
125% = 1.25 = 5/4
Express 1,250,000 in scientific notation
1,250,000 = 1.25 × 106
Express 72,000 in scientific notation and find its GCD with 180
72,000 = 7.2 × 104
GCD(72,000, 180) = 180
Prove if 2,187 is divisible by 9 and 11
2,187 → digits sum 18 → divisible by 9 (✔)
11-test: (2−1+8−7)=2 ≠ 0, ±11 → not divisible by 11 (✘).
Find the GCD of 198, 270, and 342
GCD(198, 270, 342) = 18
Express 1.875 as a fraction in simplest form and as a percentage.
1.875 = 15/8 = 187.5%.
Express 0.00032 in scientific notation
0.00032 = 3.2 × 10-4.
Express 0.0045 in scientific notation and check if 450 is divisible by 9
0.0045 = 4.5 × 10^-3; 450 → digits sum 9 → divisible by 9 (✔)
Find all numbers (less than 35) that divide evenly into 360.
Divisors of 360 less than 35 → {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30}.
Find the GCD of 567 and 1,008
GCD(567, 1,008) = 63
Write 7/16 as a decimal (to 4 decimal places) and as a percentage.
7/16 = 0.4375 = 43.75%.
Express 0.00000000047 in scientific notation
0.00000000047 = 4.7 × 10-10
Express 999999 in scientific notation and find its GCD with 81
999999 = 9.99999 × 105
GCD(999,999, 81) = 27.