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Write the prime factorisation and prime factors of 48.

Important Questions on Factors and Rational Numbers

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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Find the smallest positive integer n≥10 such that n+6 is a prime and 9n+7 is a perfect square.
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
A two-digit number ab¯ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits a & b. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. The last number is :
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
The prime numbers a, b and c are such that a+b2=4c2. Determine the sum of all possible values of a+b+c.
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
For an integer n, let Sn=n+1,n+2,…., n+18. Which of the following is true for all n≥10 ?
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Let N denote the number of all natural numbers n such that n is divisible by a prime p>n and p<20. What is the value of N?
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
A prime number p is called special if there exist primes p1, p2, p3, p4 such that p=p1+p2=p3-p4.
The number of special primes is
 
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Express 120 as a product of its prime factors.
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Which of the following number is an odd and prime number?
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
The sum of the squares of the digits of the largest two-digit prime number is:
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
If a and b are positive integers such that a2-b2 is a prime number, then a2-b2 is equal to:
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
The number of 6-digit numbers of the form ababab (in base 10) each of which is a product of exactly 6 distinct primes is
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
It is given that the number 43361 can be written as a product of two distinct prime numbers p1, p2. Further, assume that there are 42900 numbers which are less than 43361 and are co-prime to it. Then, p1+p2 is
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Consider the set E={5,6,7,8,9}. For any partition {A,B} of E, with both A and B non-empty, consider the number obtained by adding the product of elements of A to the product of elements of B. Let N be the largest prime number among these numbers. Find the sum of the digits of N.
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Express 120 as a product of its prime factors.
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
The number of prime numbers which are less than 100 is:
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
For a,b∈0,1,⋯,9, a two digit number ab is defined for 10a+b. A two digit number ab is called a special prime if both ab and ba are primes. Then the total number of special primes is
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Which of the following is not a pair of prime numbers ?
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
Suppose a,b,c are positive integers such that 2a+4b+8c=328. Then a+2b+3cabc is equal to-
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Mathematics>Arithmetic>Factors and Rational Numbers>Prime Factors
If a and b are positive integers such that a2-b2 is a prime number, then