1. It is the smallest number with exactly 10 divisors. Its divisors are- 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
2. It is the smallest even number that can be expressed as a sum of two primes in 5 different ways.
48 = 5 + 43 = 11 + 37 = 7 + 41 = 17+ 31 = 19 + 29
3. It is equal to number of hours in 2 days.
4. The square of 48 can be expressed as the sum of squares of 9 terms of an AP of common difference 3.
48^2 = 2^2 + 5^2 + 8^2 + 11^2+ 14^2 + 17^2 + 20^2 + 23^2 + 26^2
5. It is a Harshad number. Harshad number is divided by the sum of its digits.
48 ÷ 12 (4 + 8) = 4
6. The product of all proper divisors of 48 is equal to 48^4.
48^4 = 1 x 2 x 3 x 4 x 6 x 8 x 12 x 16 x 24 = 5308416
7. The atomic number of Cadmium is 48.
8. It is an abundant number.
9. It is a 17- gonal number.
10. The Rhombicuboctahedron is an Archimedan solids with 48 edges.
Dr Rajesh Kumar Thakur
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