## Skill Check VI: IITJEE Foundation Math

A) Find all the factors of the following numbers: 42, 66, 88, 180, 810.

B) Use prime tree factorization to find the factors of : 1122, 2211, 2121, 8181, 8000.

C) Find the HCF of the following numbers by prime factorization: (a) 88 and 99 (b) 84 and 108 (c) 80 and 96 (d) 208 and 234

D) Find the HCF or GCD of the following numbers by Euclid’s Long Division Method: (a) 432, 540, and 648 (b) 408, 476, and 510 (c) 1350 and 1800 (d) 3600 and 5400 (e) 7560 and 8820 (f) 7920 and 8910 (g) 14112 and 12936 (h) 25740 and 24024 (i) 108, 288, and 360 (j) 1056, 1584, and 2178

E) Find the HCF or GCD of the following numbers by Euclid’s Long Division Method: (a) 1701, 1575, and 2016 (b) 4680, 4160, and 5200 (c) 3168. 3432, and 3696 (d) 4752, 5184, and 5616 (e) 8640, 10368, 12096 (f) 9072, 8400, 9744

F) Find the greatest number that divides 10368, 9504 and 11232 exactly leaving no remainders.

G) Find the greatest number that divides 7355, 8580, and 9805 leaving exactly 5 as a remainder in each case.

H) Find the greatest number that divides 9243 and 12325 leaving exactly 3 and 5 as remainders respectively.

I) What would be the length of the the longest tape that can be used to measure the length and breadth of an auditorium 204 feet wide and 486 feet long in an exact number of times.

J) A big cardboard picture 126 cm wide and 135 cm long is to be cut up into square pieces to create a jigsaw puzzle. How many small pieces would go on to make the jigsaw puzzle if each piece is to be equal and of the maximum possible size?

K) Square placards need to be cut out from a rectangular piece of cardboard 60 inches wide and 72 inches long. What is the maximum number of equal sized placards of the biggest possible size that can be cut out? What would be the length of each placard?

L) Three ribbons, 171 cm, 185 cm, and 199 cm long are to be cut into equal pieces of maximum possible length, leaving bits of ribbons 3 cm long from each. What would be the length of each piece of ribbon and how many such pieces can one get ?

M) The capacities of two emtpy water tanks are 504 litres and 490 litres. What would be the maximum capacity of a bucket that can be used an exact number of times to fill the tanks? How many bickets full of water will be needed?

Regards,

Nalin Pithwa

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