The total number of factors of a number
which is a multiple of both 13 and 100, but is
less than 2,000 is:
Answers
Answer:
18
Step-by-step explanation:
1300 is the only common multiple of 13 and 100 with a value less than 2000
1300 = 1 x 1300
= 2 x 650
= 4 x 325
= 5 x 260
= 10 x 130
= 13 x 100
= 20 x 65
= 25 x 52
= 26 x 50
1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300 are the factors of 1300
∴ 1300 has 18 factors
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Given : a number which is a multiple of both 13 and 100, but is less than 2,000
To Find : total number of factors
Solution:
13 and 100 are co prime
a number which is a multiple of both 13 and 100 = 1300k
it is less than 2,000
Hence 1300 is only possible number
1300 = 2 * 2 * 5 * 5 * 13
1300 = 2² * 5² * 13¹
Number of factors = (2 + 1)(2 + 1) (1 + 1)
= 3 * 3 * 2
= 18
1
2
4
5
10
13
25
26
50
52
65
100
130
260
325
650
1300
There are 18 factors of a number which is a multiple of both 13 and 100, but is less than 2,000
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