The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is HCF (525, 3000)? Justify your answer.
A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify your answer.
Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.
“The product of three consecutive positive integers is divisible by 6”. Is this statement true or false”? Justify your answer.
“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons.
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer.
The decimal expansion of the rational number 14587/1250 will terminate after:
(A) one decimal place (B) two decimal places
(C) three decimal places (D) four decimal places
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