Number Theory

Problem 201

What is $\frac{12}{22}+\frac{1}{11}$ ? Give your answer in its lowest terms.

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Problem 202

15) The LCM of $29^{9}$ and $29^{11}$ is a) $29^{9}$ b) $29^{11}$ c) $29^{20}$ d) $29^{99}$ e) 29

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Problem 203

( 20 علمة) السؤال الثاني: 1- 1- برهن باسنتغام جدول الصو اب أن 2- برهن أن (20 علامة) السوال الثالث:

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Problem 204

Find the number of pennies Jorge has if he has 1 leftover penny when divided by 2, 3, or 5, and 3 leftover when divided by 4.

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Problem 205

Find the number of pennies Louisa has if:
1. $n \equiv 1 \mod 2$ ,
2. $n \equiv 1 \mod 3$ ,
3. $n \equiv 1 \mod 4$ ,
4. $n \equiv 1 \mod 6$ ,
5. $n \equiv 2 \mod 5$ .

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Problem 206

Determine if the number 57 is prime or composite.

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Problem 207

1. Prove that $2+3 \sqrt{3}$ is an irrational number. It is given that $\sqrt{ } 3$ is an irrational number.

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Problem 208

```latex \text{Greatest Common Factor (GCF) Maze!}
\text{Directions: Find the GCF of each set of numbers. Use your solutions to navigate through the maze.}
\text{SHOW ALL WORK on a separate sheet of paper and attach it to this page!}
\text{Find the GCF of the following set of numbers:}
\begin{itemize} \item 12 and 78 \end{itemize}
\text{(c) Gina Wilson (All Things Algebra\textregistered), LLC, 2019} ```

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Problem 209

Bài 13: Để phòng chống dịch Covid - 19. Tỉnh Bà Rịa-Vũng Tàu đã thành lập các đội phản úng nhanh bao gồm 16 bác sĩ hồi sức cấp cứu, 24 bác sĩ đa khoa và 40 điều dưỡng viên. Hỏi có thề thành lập nhiều nhất bao nhiêu đội phản ứng nhanh, trong đó các bác sĩ và điều dưỡng viên chia đều vào mỗi đội.

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Problem 210

(42) Find the smallest positive integer which leaves the remainder 1 when divided by $2,3,4,5,6$ , and the remainder 0 when divided by 7 .

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Problem 211

Finding the LCM
The table shows the first five multiples for the numbers 3 The LCM of 3 and 6 is and 6. \begin{tabular}{|c|c|} \hline Number & \multicolumn{1}{|c|}{ Multiples } \\ \hline 3 & $3,6,9,12,15, \ldots$ \\ \hline 6 & $6,12,18,24,30, \ldots$ \\ \hline \end{tabular}

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Problem 212

When the expression $15^{6} \times 28^{9} \times 35^{3}$ is evaluated, it ends with several consecutive zeros. How many?

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Problem 213

The prime factor trees for 70 and 385 are given below. se the prime factor trees to find the highest common factor (HCF) of 70 and 385 .

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Problem 214

The prime factor tree for 693 is given below. Draw the prime factor tree for 330 and use it to work out the highest common factor (HCF) of 330 and 693 .

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Problem 215

(4)) Shanti has 32 toys and 40 erasers to divide into prize bags for her friends. Shanti wants each prize bag to have the same number of toys and the same number of erasers. 4) What is the greatest number of prize bags Shanti can make? 41) Use the number pad to enter your answer in the box. (4) The greatest number of prize bags Shanti can make is $\square$

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Problem 216

What is the probability of guessing a correct 5-digit pin code from a 7-key keypad on the first try? Simplify your answer.

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Problem 217

(1) Oxygen atoms don't take positive oxidation number except on binding with $\qquad$ (a) Fluorine ${ }^{2} F$ (b) Chlorine ${ }_{17} \mathrm{Cl}$ (c) Hydrogen ${ }_{1} H$ (c) Sulphur ${ }_{16 S} S$

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Problem 218

Find the prime factorization of 676, using exponents for repeated factors.

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Problem 219

Find the common divisor of 70 and 385.

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Problem 220

Q22 Solve the linear congruence $13 x \equiv 2(\bmod 2 \cdot 3.5)$ by solving the system $\begin{array}{l} 13 x \equiv 2(\bmod 2) \\ 13 x \equiv 2(\bmod 3) \\ 13 x \equiv 2(\bmod 5) \end{array}$

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1 2 3

Number Theory

Problem 201

What is $\frac{12}{22}+\frac{1}{11}$ ? Give your answer in its lowest terms.

Problem 202

15) The LCM of $29^{9}$ and $29^{11}$ is a) $29^{9}$ b) $29^{11}$ c) $29^{20}$ d) $29^{99}$ e) 29

Problem 203

( 20 علمة) السؤال الثاني: 1- 1- برهن باسنتغام جدول الصو اب أن 2- برهن أن (20 علامة) السوال الثالث:

Problem 204

Find the number of pennies Jorge has if he has 1 leftover penny when divided by 2, 3, or 5, and 3 leftover when divided by 4.

Problem 205

Find the number of pennies Louisa has if:
1. $n \equiv 1 \mod 2$ ,
2. $n \equiv 1 \mod 3$ ,
3. $n \equiv 1 \mod 4$ ,
4. $n \equiv 1 \mod 6$ ,
5. $n \equiv 2 \mod 5$ .

Problem 206

Determine if the number 57 is prime or composite.

Problem 207

1. Prove that $2+3 \sqrt{3}$ is an irrational number. It is given that $\sqrt{ } 3$ is an irrational number.

Problem 208

Problem 209

Problem 210

(42) Find the smallest positive integer which leaves the remainder 1 when divided by $2,3,4,5,6$ , and the remainder 0 when divided by 7 .

Problem 211

Finding the LCM
The table shows the first five multiples for the numbers 3 The LCM of 3 and 6 is and 6. \begin{tabular}{|c|c|} \hline Number & \multicolumn{1}{|c|}{ Multiples } \\ \hline 3 & $3,6,9,12,15, \ldots$ \\ \hline 6 & $6,12,18,24,30, \ldots$ \\ \hline \end{tabular}

Problem 212

When the expression $15^{6} \times 28^{9} \times 35^{3}$ is evaluated, it ends with several consecutive zeros. How many?

Problem 213

The prime factor trees for 70 and 385 are given below. se the prime factor trees to find the highest common factor (HCF) of 70 and 385 .

Problem 214

The prime factor tree for 693 is given below. Draw the prime factor tree for 330 and use it to work out the highest common factor (HCF) of 330 and 693 .

Problem 215

Problem 216

What is the probability of guessing a correct 5-digit pin code from a 7-key keypad on the first try? Simplify your answer.

Problem 217

(1) Oxygen atoms don't take positive oxidation number except on binding with $\qquad$ (a) Fluorine ${ }^{2} F$ (b) Chlorine ${ }_{17} \mathrm{Cl}$ (c) Hydrogen ${ }_{1} H$ (c) Sulphur ${ }_{16 S} S$

Problem 218

Find the prime factorization of 676, using exponents for repeated factors.

Problem 219

Find the common divisor of 70 and 385.

Problem 220

Q22 Solve the linear congruence $13 x \equiv 2(\bmod 2 \cdot 3.5)$ by solving the system $\begin{array}{l} 13 x \equiv 2(\bmod 2) \\ 13 x \equiv 2(\bmod 3) \\ 13 x \equiv 2(\bmod 5) \end{array}$

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Number Theory

Problem 201

What is 1222+111\frac{12}{22}+\frac{1}{11}2212​+111​ ? Give your answer in its lowest terms.

Problem 202

15) The LCM of 29929^{9}299 and 291129^{11}2911 is a) 29929^{9}299 b) 291129^{11}2911 c) 292029^{20}2920 d) 299929^{99}2999 e) 29

Problem 203

( 20 علمة) السؤال الثاني: 1- 1- برهن باسنتغام جدول الصو اب أن 2- برهن أن (20 علامة) السوال الثالث:

Problem 204

Find the number of pennies Jorge has if he has 1 leftover penny when divided by 2, 3, or 5, and 3 leftover when divided by 4.

Problem 205

Find the number of pennies Louisa has if: 1. n≡1mod 2n \equiv 1 \mod 2n≡1mod2, 2. n≡1mod 3n \equiv 1 \mod 3n≡1mod3, 3. n≡1mod 4n \equiv 1 \mod 4n≡1mod4, 4. n≡1mod 6n \equiv 1 \mod 6n≡1mod6, 5. n≡2mod 5n \equiv 2 \mod 5n≡2mod5.

Problem 206

Determine if the number 57 is prime or composite.

Problem 207

1. Prove that 2+332+3 \sqrt{3}2+33​ is an irrational number. It is given that 3\sqrt{ } 3​3 is an irrational number.

Problem 208

Problem 209

Problem 210

(42) Find the smallest positive integer which leaves the remainder 1 when divided by 2,3,4,5,62,3,4,5,62,3,4,5,6, and the remainder 0 when divided by 7 .

Problem 211

Problem 212

When the expression 156×289×35315^{6} \times 28^{9} \times 35^{3}156×289×353 is evaluated, it ends with several consecutive zeros. How many?

Problem 213

The prime factor trees for 70 and 385 are given below. se the prime factor trees to find the highest common factor (HCF) of 70 and 385 .

Problem 214

The prime factor tree for 693 is given below. Draw the prime factor tree for 330 and use it to work out the highest common factor (HCF) of 330 and 693 .

Problem 215

Problem 216

What is the probability of guessing a correct 5-digit pin code from a 7-key keypad on the first try? Simplify your answer.

Problem 217

(1) Oxygen atoms don't take positive oxidation number except on binding with \qquad (a) Fluorine 2F{ }^{2} F2F (b) Chlorine 17Cl{ }_{17} \mathrm{Cl}17​Cl (c) Hydrogen 1H{ }_{1} H1​H (c) Sulphur 16SS{ }_{16 S} S16S​S

Problem 218

Find the prime factorization of 676, using exponents for repeated factors.

Problem 219

Find the common divisor of 70 and 385.

Problem 220

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What is $\frac{12}{22}+\frac{1}{11}$ ? Give your answer in its lowest terms.

15) The LCM of $29^{9}$ and $29^{11}$ is a) $29^{9}$ b) $29^{11}$ c) $29^{20}$ d) $29^{99}$ e) 29

Find the number of pennies Louisa has if:
1. $n \equiv 1 \mod 2$ ,
2. $n \equiv 1 \mod 3$ ,
3. $n \equiv 1 \mod 4$ ,
4. $n \equiv 1 \mod 6$ ,
5. $n \equiv 2 \mod 5$ .

1. Prove that $2+3 \sqrt{3}$ is an irrational number. It is given that $\sqrt{ } 3$ is an irrational number.

(42) Find the smallest positive integer which leaves the remainder 1 when divided by $2,3,4,5,6$ , and the remainder 0 when divided by 7 .

When the expression $15^{6} \times 28^{9} \times 35^{3}$ is evaluated, it ends with several consecutive zeros. How many?

(1) Oxygen atoms don't take positive oxidation number except on binding with $\qquad$ (a) Fluorine ${ }^{2} F$ (b) Chlorine ${ }_{17} \mathrm{Cl}$ (c) Hydrogen ${ }_{1} H$ (c) Sulphur ${ }_{16 S} S$