Advertisements
Advertisements
प्रश्न
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Advertisements
उत्तर
Numbers are of two types - prime and composite. Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 and itself.
It can be observed that,
7 × 11 × 13 + 13
= 13 (7 × 11 + 1)
= 13 × (77 + 1)
= 13 × 78
= 3 × 13 × 6
The given expression has 6 and 13 as its factors. Therefore, it is a composite number.
7 × 6 × 5 × 4 × 3 × 2 × 1 + 5
= 5 × (7 × 6 × 4 × 3 × 2 × 1 + 1)
= 5 × (1008 + 1)
= 5 × 1009
1009 cannot be factorized further. Therefore, the given expression has 5 and 1009 as its factors. Hence, it is a composite number.
APPEARS IN
संबंधित प्रश्न
Find the LCM and HCF of the following integers by applying the prime factorisation method:
84, 90 and 120
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 sum of the exponents of prime factors in the prime factorization of 98.
If the product of two numbers is 1080 and their HCF is 30, find their LCM.
Find the LCM and HCF of the following integers by applying the prime factorisation method.
8, 9 and 25
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
Find the L.C.M. and H.C.F. of 408 and 170 by applying the fundamental theorem of Arithmetic
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?
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 ______.
According to the fundamental theorem of arithmetic, if T (a prime number) divides b2, b > 0, then ______.
If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is ______.
If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
If two positive integers a and b are written as a = x3 y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is ______.
The LCM of smallest 2-digit number and smallest composite number is ______.
If n is a natural number, then 8n cannot end with digit
The HCF of the smallest 2-digit number and the smallest composite number is ______.
