
The number of prime numbers between 11 and 60 is ____.
The numbers 29 and ____ are twin primes.
3753 is divisible by 9 and hence divisible by ____.
The number of distinct prime factors of the smallest 4-digit number is ____.
The sum of distinct prime factors of 30 is ____.
Answer
511.5k+ views
Hint: First list all the prime numbers which lie between 11 and 60. Then count the numbers.
The twin prime of 29 is 31.
Factorize the smallest 4-digit number and count the distinct prime factor.
Factorize the number 30 and add all the distinct prime factors.
Complete step-by-step answer:
The prime numbers between 11 and 60 are 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59.
There are a total of 12 prime numbers that lie between 11 and 60.
Hence, the number of prime numbers between 11 and 60 is 12.
A twin prime is a prime number that differs by 2 from another prime number.
The numbers that differ by 2 from 29 are 27 and 31.
As 27 is not a prime number only 31 is a prime number.
Hence, the numbers 29 and 31 are twin primes.
As 3753 is divisible by 9 and 9 is divisible by 3.
Hence, 3753 is divisible by 9 and hence divisible by 3.
The smallest 4-digit number is 1000.
The smallest number by which 1000 is divisible is 2. Then,
The smallest number by which 500 is divisible is 2. Then,
The smallest number by which 250 is divisible is 2. Then,
The smallest number by which 125 is divisible is 5. Then,
The smallest number by which 25 is divisible is 5. Then,
So, the distinct prime factors of 1000 are 2 and 5.
Hence, the number of distinct prime factors of the smallest 4-digit number is 2.
The smallest number by which 30 is divisible is 2. Then,
The smallest number by which 15 is divisible is 3. Then,
So, the distinct prime factors of 1000 are 2 and 5.
The sum of distinct prime factors is,
Hence, the sum of distinct prime factors of 30 is 10.
Note: Students must exclude 11 as it is mentioned the prime numbers between 11 and 60.
The students must know the meaning of twin primes to find the twin primes of 29.
The student must not go for the division of 3753 by 9 to find other factors of 3753.
Students must not count all prime factors or all factors of 4-digit numbers as it is mentioned about distinct prime factors.
The twin prime of 29 is 31.
Factorize the smallest 4-digit number and count the distinct prime factor.
Factorize the number 30 and add all the distinct prime factors.
Complete step-by-step answer:
The prime numbers between 11 and 60 are 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59.
There are a total of 12 prime numbers that lie between 11 and 60.
Hence, the number of prime numbers between 11 and 60 is 12.
A twin prime is a prime number that differs by 2 from another prime number.
The numbers that differ by 2 from 29 are 27 and 31.
As 27 is not a prime number only 31 is a prime number.
Hence, the numbers 29 and 31 are twin primes.
As 3753 is divisible by 9 and 9 is divisible by 3.
Hence, 3753 is divisible by 9 and hence divisible by 3.
The smallest 4-digit number is 1000.
The smallest number by which 1000 is divisible is 2. Then,
The smallest number by which 500 is divisible is 2. Then,
The smallest number by which 250 is divisible is 2. Then,
The smallest number by which 125 is divisible is 5. Then,
The smallest number by which 25 is divisible is 5. Then,
So, the distinct prime factors of 1000 are 2 and 5.
Hence, the number of distinct prime factors of the smallest 4-digit number is 2.
The smallest number by which 30 is divisible is 2. Then,
The smallest number by which 15 is divisible is 3. Then,
So, the distinct prime factors of 1000 are 2 and 5.
The sum of distinct prime factors is,
Hence, the sum of distinct prime factors of 30 is 10.
Note: Students must exclude 11 as it is mentioned the prime numbers between 11 and 60.
The students must know the meaning of twin primes to find the twin primes of 29.
The student must not go for the division of 3753 by 9 to find other factors of 3753.
Students must not count all prime factors or all factors of 4-digit numbers as it is mentioned about distinct prime factors.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

Explain land use pattern in India and why has the land class 8 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE
