Question
Explain why 3 × 5 × 7 + 7 is a composite number.
✓
Answer
We have, 3 × 5 × 7 + 7 = 105 + 7 = 112
Now, $112 = 2 \times 2 \times 2 \times 2 \times 7 = 2^4 \times 7$
So, it is the product of prime factors 2 and 7. i.e., it has more than two factors.
Hence, it is a composite number.
Now, $112 = 2 \times 2 \times 2 \times 2 \times 7 = 2^4 \times 7$
So, it is the product of prime factors 2 and 7. i.e., it has more than two factors.
Hence, it is a composite number.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the equation $\left(1+m^2\right) x^2+2 m c x+\left(c^2-a^2\right)=0$ has equal roots, prove that $c^2=a^2\left(1+m^2\right)$.
→Which term of the arithmetic progression 8, 14, 20, 26, ... will be 72 more than its $41^{st}$ term.
→Find the area of a quadrant of a circle hose circumference is 44cm.
Solve the following quadratic equation:
$\frac{\text{x}}{\text{x}+1}+\frac{\text{x}+1}{\text{x}}=2\frac{4}{15},$ $\text{x}\neq0,-1$
→$\frac{\text{x}}{\text{x}+1}+\frac{\text{x}+1}{\text{x}}=2\frac{4}{15},$ $\text{x}\neq0,-1$
In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
→$x - 3y = 3$
$3x - 9y = 2$
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Two different dice are thrown together. Find the probability that:
-
The sum of the numbers appeared is less than 7.
-
The product of the numbers appeared is less than 18.
Find the roots of the following equations, if they exist, by applying the quadratic formula:
$x^2 + 6x - (a^2 + 2a -8) = 0$
→$x^2 + 6x - (a^2 + 2a -8) = 0$
A boy whose eye level is $1.35 m$ from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is $60^{\circ}$. After $12$ seconds, the angle of elevation reduces to $30^{\circ}$. If the speed of the wind is $3 m / s$ then find the height of the balloon from the ground. $($Use $\sqrt{3}=1.73)$
→In the figure, OQ:PQ = 3:4 and perimeter of $\triangle\text{POQ}$ = 60cm. Determine PQ, QR and OP.
→