Advertisements
Advertisements
Question
Show that 12n cannot end with the digit 0 or 5 for any natural number n.
Advertisements
Solution
If any number ends with the digit 0 or 5, it is always divisible by 5.
If 12n ends with the digit zero or five it must be divisible by 5.
This is possible only if prime factorisation of 12n contains the prime number 5.
Now, 12 = 2 × 2 × 3 = 22 × 3
12n = (22 × 3)n = 22n × 3n
Since, there is no term containing 5.
Hence, there is no value of n ∈ N for which 12n ends with the digit zero or five.
APPEARS IN
RELATED QUESTIONS
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
State fundamental theorem of arithmetic.
Find the LCM and HCF of the following integers by applying the prime factorisation method:
24, 15 and 36
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where m, n are non-negative integers.
\[\frac{3}{8}\]
Write the exponent of 2 in the prime factorization of 144.
Write the sum of the exponents of prime factors in the prime factorization of 98.
For what value of natural number n, 4n can end with the digit 6?
Find the L.C.M. and H.C.F. of 408 and 170 by applying the fundamental theorem of Arithmetic
The sum of the exponents of the prime factors in the prime factorization of 1729 is
LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by ______.
For some integer q, every odd integer is of the form ______.
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
Explain why 3 × 5 × 7 + 7 is a composite number.
If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is ______.
Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.
Statement R (Reason): HCF is always a factor of LCM.
Show the 6n cannot end with digit 0 for any natural number 'n'.
The LCM of smallest 2-digit number and smallest composite number is ______.
National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?
