Which of the following numbers is not a facto | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) number $x$ is a factor of $5^{p} 7^{q}$ if and only if the prime factorization of $x$ contains only the primes $5$ and $7$,with exponents less tha

Vedclass · Accepted Answer

$735$

Vedclass · Answer

(D) number $x$ is a factor of $5^{p} 7^{q}$ if and only if the prime factorization of $x$ contains only the primes $5$ and $7$,with exponents less than or equal to $p$ and $q$ respectively.Given the expression $5^{p} 7^{q}$,any factor must be of the form $5^{a} 7^{b}$ where $0 \leq a \leq p$ and $0 \leq b \leq q$.Let's analyze the prime factorization of the given options:$A) 35 = 5^1 	imes 7^1$. This is a factor if $p \geq 1$ and $q \geq 1$.$B) 175 = 5^2 	imes 7^1$. This is a factor if $p \geq 2$ and $q \geq 1$.$C) 1225 = 5^2 	imes 7^2$. This is a factor if $p \geq 2$ and $q \geq 2$.$D) 735 = 5^1 	imes 7^2 	imes 3^1$. Since $735$ contains a prime factor $3$,which is not present in the expression $5^{p} 7^{q}$,it can never be a factor regardless of the values of $p$ and $q$ (provided $p, q 
eq 0$ as given).Therefore,$735$ is not a factor.

Which of the following numbers is not a factor of $5^{p} 7^{q}$ where $p \neq 0$ and $q \neq 0$?

Similar Questions

What will come in the place of the question mark $(?)$ in the following expression?
$3 \frac{3}{4} + 4 \frac{2}{5} - 3 \frac{1}{8} = ?$

If the sum of squares of two real numbers is $41$ and their sum is $9,$ then the sum of cubes of these two numbers is

What should come in place of the question mark $(?)$ in the following equation?
$39.97 \%$ of $649.8 \div 13.05 = 45.12 - ?$

$1 . \overline{27}$ in the form $\frac{p}{q}$ is equal to

Along a yard $225 \ m$ long,$26$ trees are planted at equal distances,with one tree at each end of the yard. What is the distance between two consecutive trees in meters?

Vedclass Test Series

Exam Paper Generator

Online Exam Module