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The greatest number of four digits that is divisible by 30,36,45, and 75 is:
- a)9990
- b)9900
- c)9930
- d)9936
Correct answer is option 'B'. Can you explain this answer?
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The greatest number of four digits that is divisible by30,36,45, and75...
Problem:
The greatest number of four digits that is divisible by 30, 36, 45, and 75 is:
a) 9990
b) 9900
c) 9930
d) 9936
Solution:
To find the greatest number of four digits that is divisible by 30, 36, 45, and 75, we need to find the least common multiple (LCM) of these numbers.
Finding the LCM:
To find the LCM of 30, 36, 45, and 75, we can use the prime factorization method.
1. Prime factorize each number:
- 30 = 2 × 3 × 5
- 36 = 2^2 × 3^2
- 45 = 3^2 × 5
- 75 = 3 × 5^2
2. Identify the highest power of each prime factor among the numbers:
- 2^2, 3^2, 5^2
3. Multiply the highest powers of each prime factor:
LCM = 2^2 × 3^2 × 5^2 = 4 × 9 × 25 = 900
Finding the greatest four-digit number divisible by 900:
To find the greatest four-digit number divisible by 900, we need to find the largest multiple of 900 that is less than 10,000.
Divide 10,000 by 900:
10000 ÷ 900 = 11 remainder 100
Since the remainder is 100, subtract it from 10,000:
10,000 - 100 = 9,900
Thus, the greatest four-digit number divisible by 900 is 9,900.
Final Answer:
Therefore, the correct option is b) 9900.
The greatest number of four digits that is divisible by 30, 36, 45, and 75 is:
a) 9990
b) 9900
c) 9930
d) 9936
Solution:
To find the greatest number of four digits that is divisible by 30, 36, 45, and 75, we need to find the least common multiple (LCM) of these numbers.
Finding the LCM:
To find the LCM of 30, 36, 45, and 75, we can use the prime factorization method.
1. Prime factorize each number:
- 30 = 2 × 3 × 5
- 36 = 2^2 × 3^2
- 45 = 3^2 × 5
- 75 = 3 × 5^2
2. Identify the highest power of each prime factor among the numbers:
- 2^2, 3^2, 5^2
3. Multiply the highest powers of each prime factor:
LCM = 2^2 × 3^2 × 5^2 = 4 × 9 × 25 = 900
Finding the greatest four-digit number divisible by 900:
To find the greatest four-digit number divisible by 900, we need to find the largest multiple of 900 that is less than 10,000.
Divide 10,000 by 900:
10000 ÷ 900 = 11 remainder 100
Since the remainder is 100, subtract it from 10,000:
10,000 - 100 = 9,900
Thus, the greatest four-digit number divisible by 900 is 9,900.
Final Answer:
Therefore, the correct option is b) 9900.
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Community Answer
The greatest number of four digits that is divisible by30,36,45, and75...
Given:
The greatest number of four digits that is divisible by 30,36,45, and 75:
Using the L.C.M. method,
LCM of (30,36,45,75) = 900
⇒ 2×2×3×3×5×5
The greatest number of four digits is 9999.
The greatest number of four-digit which is exactly divisible by 30,36,45,75 = 9999−99
= 9900
The greatest number of four digits that is divisible by 30,36,45, and 75:
Using the L.C.M. method,
LCM of (30,36,45,75) = 900
⇒ 2×2×3×3×5×5
The greatest number of four digits is 9999.
The greatest number of four-digit which is exactly divisible by 30,36,45,75 = 9999−99
= 9900
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The greatest number of four digits that is divisible by30,36,45, and75is:a)9990b)9900c)9930d)9936Correct answer is option 'B'. Can you explain this answer?
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