Number Theory

Problem 101

Find the greatest common divisor (GCD) of given number pairs: $\operatorname{gcd}(132,156)$ , $\operatorname{gcd}(65,85)$ , and $\operatorname{gcd}(120,168)$ .

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Problem 102

Find the complement of the binary number $1010101$ . Calculate the magnitude and show all steps.

See Solution

Problem 103

Find the value of $9^{-2}$ .

See Solution

Problem 104

Find the second number that, when multiplied with $\frac{7}{3}$ , results in an irrational product. Options: $\frac{3}{7}$ , $2 \pi$ , 1, $\sqrt{3}$ .

See Solution

Problem 105

Encuentra el máximo común divisor de $9$ y $36$ .

See Solution

Problem 106

Determine if each number is prime or composite, and explain your reasoning. $27, 19, 31, 38, 45, 53, 87, 93$

See Solution

Problem 107

Find the value of $i^{52}$ , where $i$ is the imaginary unit.

See Solution

Problem 108

Fill the blank with either $\in$ or $\notin$ to make the statement true: $-29 \in \{9,17,29,31\}$

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Problem 109

Find the square root of -15.

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Problem 110

Demuestra que si $a$ es impar, entonces $a^2 + 3a + 5$ es impar.

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Problem 111

Solve the riddle: "I am the start of everything, the end of everywhere. I'm the start of eternity, the end of time and space. What am I?"

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Problem 112

What is the binary representation of the decimal number 12? a. 1100 b. 1110 c. 1010 d. 1101

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Problem 113

Find the base of the expression $5^{6}$ .

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Problem 114

Find the value of $0^{9}$ .

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Problem 115

Determine if any two natural numbers have at least one common factor. True or False?

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Problem 116

Arrange the numbers from left to right on a number line: $-2.76, -2.57, -2.5, -1.85, -1.58, 2.5, 2.85$ .

See Solution

Problem 117

Show that if $a$ and $b$ are relatively prime, then $\operatorname{gcd}(da, db) = d$ for any positive integer $d$ .

See Solution

Problem 118

Convert the total surface area of Africa, approximately 11,700,000 square miles, to scientific notation.

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Problem 119

Find the value of $b$ that satisfies the equation $14_b + 23_b = 40_b$ , where $b \in \{4, 5, 7\}$ .

See Solution

Problem 120

Convert $1,374,000,000$ to scientific notation.

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Problem 121

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

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Problem 122

Evaluate the factorial expression $\frac{2! \, 5!}{6! \, 3!}$ and simplify the result.

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Problem 123

Find the odd one out in the given sets. Explain your reasoning. Sets: $5,8,2,1,2,6$ , $15,18,12,11,0,16$ , $58,21,26$ , $9,4,1,3,7,5$ .

See Solution

Problem 124

Rewrite $\frac{1}{10,000}$ as a power of 10.

See Solution

Problem 125

Evaluate the natural logarithm of 1 without using a calculator: $\ln 1 = \square$

See Solution

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Number Theory

Problem 101

Find the greatest common divisor (GCD) of given number pairs: gcd⁡(132,156)\operatorname{gcd}(132,156)gcd(132,156), gcd⁡(65,85)\operatorname{gcd}(65,85)gcd(65,85), and gcd⁡(120,168)\operatorname{gcd}(120,168)gcd(120,168).

Problem 102

Find the complement of the binary number 101010110101011010101. Calculate the magnitude and show all steps.

Problem 103

Find the value of 9−29^{-2}9−2.

Problem 104

Find the second number that, when multiplied with 73\frac{7}{3}37​, results in an irrational product. Options: 37\frac{3}{7}73​, 2π2 \pi2π, 1, 3\sqrt{3}3​.

Problem 105

Encuentra el máximo común divisor de 999 y 363636.

Problem 106

Determine if each number is prime or composite, and explain your reasoning. 27,19,31,38,45,53,87,9327, 19, 31, 38, 45, 53, 87, 9327,19,31,38,45,53,87,93

Problem 107

Find the value of i52i^{52}i52, where iii is the imaginary unit.

Problem 108

Fill the blank with either ∈\in∈ or ∉\notin∈/ to make the statement true: −29∈{9,17,29,31}-29 \in \{9,17,29,31\}−29∈{9,17,29,31}

Problem 109

Find the square root of -15.

Problem 110

Demuestra que si aaa es impar, entonces a2+3a+5a^2 + 3a + 5a2+3a+5 es impar.

Problem 111

Solve the riddle: "I am the start of everything, the end of everywhere. I'm the start of eternity, the end of time and space. What am I?"

Problem 112

What is the binary representation of the decimal number 12? a. 1100 b. 1110 c. 1010 d. 1101

Problem 113

Find the base of the expression 565^{6}56.

Problem 114

Find the value of 090^{9}09.

Problem 115

Determine if any two natural numbers have at least one common factor. True or False?

Problem 116

Arrange the numbers from left to right on a number line: −2.76,−2.57,−2.5,−1.85,−1.58,2.5,2.85-2.76, -2.57, -2.5, -1.85, -1.58, 2.5, 2.85−2.76,−2.57,−2.5,−1.85,−1.58,2.5,2.85.

Problem 117

Show that if aaa and bbb are relatively prime, then gcd⁡(da,db)=d\operatorname{gcd}(da, db) = dgcd(da,db)=d for any positive integer ddd.

Problem 118

Convert the total surface area of Africa, approximately 11,700,000 square miles, to scientific notation.

Problem 119

Find the value of bbb that satisfies the equation 14b+23b=40b14_b + 23_b = 40_b14b​+23b​=40b​, where b∈{4,5,7}b \in \{4, 5, 7\}b∈{4,5,7}.

Problem 120

Convert 1,374,000,0001,374,000,0001,374,000,000 to scientific notation.

Problem 121

Find the LCM⁡\operatorname{LCM}LCM and GCF⁡\operatorname{GCF}GCF of given numbers using the list method. Additional materials: eBook.

Problem 122

Evaluate the factorial expression 2! 5!6! 3!\frac{2! \, 5!}{6! \, 3!}6!3!2!5!​ and simplify the result.

Problem 123

Find the odd one out in the given sets. Explain your reasoning. Sets: 5,8,2,1,2,65,8,2,1,2,65,8,2,1,2,6, 15,18,12,11,0,1615,18,12,11,0,1615,18,12,11,0,16, 58,21,2658,21,2658,21,26, 9,4,1,3,7,59,4,1,3,7,59,4,1,3,7,5.

Problem 124

Rewrite 110,000\frac{1}{10,000}10,0001​ as a power of 10.

Problem 125

Evaluate the natural logarithm of 1 without using a calculator: ln⁡1=□\ln 1 = \squareln1=□

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Find the greatest common divisor (GCD) of given number pairs: $\operatorname{gcd}(132,156)$ , $\operatorname{gcd}(65,85)$ , and $\operatorname{gcd}(120,168)$ .

Find the complement of the binary number $1010101$ . Calculate the magnitude and show all steps.

Find the value of $9^{-2}$ .

Find the second number that, when multiplied with $\frac{7}{3}$ , results in an irrational product. Options: $\frac{3}{7}$ , $2 \pi$ , 1, $\sqrt{3}$ .

Encuentra el máximo común divisor de $9$ y $36$ .

Determine if each number is prime or composite, and explain your reasoning. $27, 19, 31, 38, 45, 53, 87, 93$

Find the value of $i^{52}$ , where $i$ is the imaginary unit.

Fill the blank with either $\in$ or $\notin$ to make the statement true: $-29 \in \{9,17,29,31\}$

Demuestra que si $a$ es impar, entonces $a^2 + 3a + 5$ es impar.

Find the base of the expression $5^{6}$ .

Find the value of $0^{9}$ .

Arrange the numbers from left to right on a number line: $-2.76, -2.57, -2.5, -1.85, -1.58, 2.5, 2.85$ .

Show that if $a$ and $b$ are relatively prime, then $\operatorname{gcd}(da, db) = d$ for any positive integer $d$ .

Find the value of $b$ that satisfies the equation $14_b + 23_b = 40_b$ , where $b \in \{4, 5, 7\}$ .

Convert $1,374,000,000$ to scientific notation.

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

Evaluate the factorial expression $\frac{2! \, 5!}{6! \, 3!}$ and simplify the result.

Find the odd one out in the given sets. Explain your reasoning. Sets: $5,8,2,1,2,6$ , $15,18,12,11,0,16$ , $58,21,26$ , $9,4,1,3,7,5$ .

Rewrite $\frac{1}{10,000}$ as a power of 10.

Evaluate the natural logarithm of 1 without using a calculator: $\ln 1 = \square$