A number is less than 50. It is multiple of 7 it has 3 factors. which is that number
please give the correct answer please
Answers
Solution :-
checking multiple of 7 less than 50 and their factors :-
- 7 = 1 *7 = 1 and 7 = 2 factors
- 14 = 2 * 7 = 1, 2, 7 and 14 = 4 factor
- 21 = 3 * 7 = 1, 3, 7 and 21 = 4 factors
- 28 = 2 * 2 * 7 = 1, 2, 4, 7, 14 and 28 = 6 factors
- 35 = 7 * 5 = 1, 5, 7 and 35 = 4 factors
- 42 = 2 * 3 * 7 = 1, 2, 3, 6, 7, 14, 21 and 42 = 8 factors
- 49 = 7 * 7 = 1 , 7 and 49 = 3 factor .
therefore, required number is 49 .
Method 2) :-
Concept used to find total number of factors :-
when N is a composite number and a,b and c are its prime factors. Then :-
- N = a^p * b^q * c^r
- Total Number of factors = (p + 1)(q + 1)(r + 1)
checking total factors of multiple of 7
→ 7 = 1 * 7¹ = (1 + 1) = 2 factors
→ 14 = 2¹ * 7¹ = (1 + 1) * (1 + 1) = 2 * 2 = 4 factors .
→ 21 = 3¹ * 7¹ = (1 + 1) * (1 + 1) = 2 * 2 = 4 factors .
→ 28 = 2² * 7 = (2 + 1) * (1 + 1) = 3 * 2 = 6 factors .
→ 35 = 5¹ * 7¹ = (1 + 1) * (1 + 1) = 2 * 2 = 4 factors .
→ 42 = 2¹ * 3¹ * 7¹ = (1 + 1) * (1 + 1) * (1 + 1) = 2 * 2 * 2 = 8 factors .
→ 49 = 7² = (2 + 1) = 3 factors .
Hence, required number is 49 .
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Given : A number is less than 50. It is multiple of 7 it has 3 factors
To Find : the number
Solution:
Only perfect Square numbers have odd number of factors
all other number have even number of factor
As its given that
Number has 3 factors and 3 is odd hence number must be a square
As number is multiple of 7
and 7 is prime
Hence number must have square of 7
Hence 7² = 49
49 is less than 50
and factors are 1 , 7 and 49 which are 3
Hence required number is 49
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