Factors that end with zero:
Factors whose unit digit is zero or we can say factors which are divisible by 10.
Example 1: Find the number of factors of 58800 that end with 0.
Solution: If a number ends with 0 then it must have at least 21 and 51.
We first factorize 58800.
58800 = 24 315272
Hence odd factor must have
2(1 or 2 or 3or 4)—– 4 factors
3(0 or 1 ) —– 1+1=2 factors
5(1 or 2) ——- 2 factors
7(0 or 1 or 2) — 1+2=3 factors
Hence, total number of factors ending with 0 = (4)(2)(2)(3) = 48
Alternate way:
To find number of factors, which are divisible by 10 we divide the given number by 10 and then find the number of factors of the quotient.
Divide 58800=24 315272 by 10 to get 23 3151 72 and its number of factors are 4x2x2x3=48
Factors not ending with zero
Example 2: Find the number of factors of 58800 that are not ending with 0?
Solution: We first factorize 58800.
58800 = 24 315272
Total number of factors of 58800 is 5x2x3x3=90 and in previous example we calculated total number of factors ending with 0 are 48.
Number of odd factors = Total number of factors – Number of factors ending with 0 =90- 48 =42
Factors divisible by 12
Example 3: Find the number of factors of 58800, which are divisible by 12?
Solution:
Since we have to find the number of factors, which are divisible by 12,then it must have at least 22 and 31.
We first factorize 58800.
58800 = 24 315272
Hence factors divisible by 12 must have
2(2 or 3or 4)—– 3 factors
3( 1 ) —– 1 factor
5(0 or1 or 2) ——- 3 factors
7(0 or 1 or 2) — 1+2=3 factors
Hence, total number of factors, which are divisible by 12 = (3)(1)(3)(3) = 27
Alternate way:
To find number of factors, which are divisible by 12 we divide the given number by 12 and then find the number of factors of the quotient.
Divide 58800=24 315272 by 12 to get 22 52 72 and its number of factors are 3x3x3=27
