Find the numbers of factors of ${2^2} \times {10^2}$ .

Question

Vedantu Content Team · Accepted Answer

Hint:A factor is  numbers that divides a given number without leaving a remainder means it gives integer quantity . If we solve this number  ${2^2} \times {10^2}$ we get $400$, now check the numbers on which if we divide it give integers .Complete step-by-step answer:First factor means that if we divide any number with the factors of that number we get an integers for example that if number is $15$ hence its factors is $1,3,5,15$  So if we divide  $1,3,5,15$ to $15$ we get integer value ,So for the factor of ${2^2} \times {10^2}$ on solving this $4 \times 100$= $400$ So basically we have to find the factor of $400$ .So if we divide $1$ by $400$ we get $400$ it is an integer so it is factor of $400$ if we divide $2$ by $400$ we get $200$ it is an integer so it is factor of $400$if we divide $4$ by $400$ we get $100$ it is an integer so it is factor of $400$if we divide $5$ by $400$ we get $80$ it is an integer so it is factor of $400$if we divide $8$ by $400$ we get $50$ it is an integer so it is factor of $400$if we divide $10$ by $400$ we get $40$ it is an integer so it is factor of $400$if we divide $16$ by $400$ we get $25$ it is an integer so it is factor of $400$if we divide $20$ by $400$ we get $20$ it is an integer so it is factor of $400$if we divide $25$ by $400$ we get $16$ it is an integer so it is factor of $400$if we divide $40$ by $400$ we get $10$ it is an integer so it is factor of $400$if we divide $50$ by $400$ we get $8$ it is an integer so it is factor of $400$if we divide $80$ by $400$ we get $5$ it is an integer so it is factor of $400$if we divide $100$ by $400$ we get $4$ it is an integer so it is factor of $400$if we divide $200$ by $400$ we get $2$ it is an integer so it is factor of $400$if we divide $400$ by $400$ we get $1$ it is an integer so it is factor of $400$Hence ${2^2} \times {10^2}$ have $15$ factors that are $1,2,4,5,8,10,16,20,25,40,50,80,100,200,400$ and the highest factor is $400$. Note:Prime numbers are numbers that have only two factors that are one and themselves. For example, the first five prime numbers are $2,3,5,7,11$ . Those numbers which have more than two factors are called composite numbers . Prime factors are factors of a number that are, themselves, prime numbers.