# Class 10 Maths Worksheet for Real Numbers

1) In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108, respectively. Find the minimum number of rooms required if in each room the same numbers of participants are to be seated and all of them being in the same subject.
2) If the HCF of 657 and 963 is expressible in the form 657x + 963  -15, find x.
3) Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
4) Find the greatest umbers that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
5) Find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively.
6) Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
7) Find the smallest number which when increased by 17 is exactly divisible by both 520 and 468.
8) A circular field has a circumference of 360km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?
9) If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is.
10) The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other.
11) 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
(A) xy
(B) xy2
(C) x3y3
(D) x2y2
12)  If two positive integers p and q can be expressed as
p = ab2 and q a3 a, b being prime numbers, then LCM (p, q) is
(A) ab
(B) a2b2
(C)  a3b2
(D) a3b3
13) If HCF (26, 169) = 13, then LCM (26, 169) =
14) If 3 is the least prime factor of number a and 7 is the least prime factor of numbers b, then the least prime factor of a + b, is.
15) ) Euclid's Division Lemma states that if p and q are any two positive integers, then there exist unique integers r and s such that
(A) p = qr + s, 0 ≤ s < q
(B) p = qr + s, 0 < s ≤ q
(C) = qr + s, 0 ≤ r < q
(D) p = qr + s, 0 < r ≤ q
16) Two tankers contain 583 litres and 242 litres of petrol respectively. A container with maximum capacity is used which can measure the petrol of either tanker in exact number of litres. How many containers of petrol are there in the f irst tanker.
(A) 53
(B) 50
(C) 54
(D) 11
17)