The square root of how many factors of 1440 will be a
natural number
Answers
Answer : 6
Explanation
1440 = 2^5 × 3^2 × 5
So, We know that, it will have (5+1)(2+1)(1+1) factors, which sums to 6(3)(2) = 36 factors.
Let's try to list them,
1,
2,
3,
4,
5,
6,
8,
9,
10,
12,15,16,18,20,24,30,32,36,40,45,48,60,72,80,90,96,120,144,160,180,240,288,360,480,720,1440.
Out of these, 1, 4, 9, 16, 36, 144 are square numbers.
Thus, Square root of these 6 numbers will be natural numbers.
Therefore, We can conclude The square root of 6 factors of 1440 will be a natural number.
Alternatively,
We can find this from the standard form of 1440
1440 = 2^5 × 3^2 × 5
Writing down the possible,
2^2
2^4
2^2 × 3^2
2^4 × 3^2
3^2
1
So, We see 6 numbers are possible.
Answer:
1. , 4. , 9. , 16. , 36 & 144
are squares
total 6 factors
Step-by-step explanation:
to solve it into simple way
1440 = 144 * 10
1440 = (12)^2. * 10
12 = 1 * 12
12 = 2*6
12 = 3*4
1^2 = 1
2^2 = 4
3^2 =9
4^2 = 16
6^2 = 36
12^2 = 144
1. , 4. , 9. , 16. , 36 & 144
are squares
total 6 factors