Without actual division show that 11 is a factor of each of the following numbers:
Without actual division show that each of the following numbers is divisible by 5:
What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?
In a school there are two sections – section A and section B of Class VI. There are 32 students in sectionA and 36 in section B. Determine the minimum number of books required for their class library so thatthey can be distributed equally among students of section A or section B.
In a morning walk three persons step off together. Their steps measure 80cm, 85cm and 90cmrespectively. What is the minimum distance each should walk so that he can cover the distance in completesteps?
Determine the number nearest to 100000 but greater than 100000 which is exactly divisible by each of 8,15 and 21.
A school bus picking up children in a colony of flats stops at every sixth block of flats. Another schoolbus starting from the same place stops at every eighth blocks of flats. Which is the first bus stop at whichboth of them will stop?
Telegraph poles occur at equal distances of 220m along a road and heaps of stones are put at equaldistances of 300m along the same road. The first heap is at the foot of the first pole. How far from it alongthe road is the next heap which lies at the foot of a pole?
For each of the following pairs of numbers, verify the property:
Product of the number = Product of their HCF and LCM
Find the HCF and LCM of the following pairs of numbers:
The LCM and HCF of two numbers are 180 and 6 respectively. If one of the numbers is 30, find theother number.
What is the smallest odd prime? Is every odd number a prime number? If not, give an example of an oddnumber which is not prime.
What are composite numbers? Can a composite number be odd? If yes, write the smallest odd compositenumber.
What are co-primes? Give examples of five pairs of co-primes. Are co-primes always prime? If no,illustrate your answer by an example.
Which of the following pairs are always co-prime?
(i)two prime numbers
(ii)one prime and one composite number
(iii)two composite numbers
Find the possible missing twins for the following numbers so that they become twin primes:
A list consists of the following pairs of numbers:
(i)51, 53; 55, 57; 59, 61; 63, 65; 67, 69; 71, 73
Categorize them as pairs of
State true (T) or false (F):
(i)The sum of primes cannot be a prime.
(ii)The product of primes cannot be a prime.
(iii)An even number is composite.
(iv)Two consecutive numbers cannot be both primes.
(v)Odd numbers cannot be composite.
(vi)Odd numbers cannot be written as sum of primes.
(vii)A number and its successor are always co-primes.
In which of the following expressions, prime factorization has been done?
(i)24 = 2 × 3 × 4
(ii)56 = 1 × 7 × 2 × 2 × 2
(iii)70 = 2 × 5 × 7
(iv)54 = 2 × 3 × 9
Determine prime factorization of each of the following numbers:
Find the prime factors of 1729. Arrange the factors in ascending order, and find the relation between twoconsecutive prime factors.
In each of the following numbers, replace * by the smallest number to make it divisible by 3:
(i)75 * 5
(ii)35 * 64
(iii)18 * 71
In each of the following numbers, replace * by the smallest number to make it divisible by 9:
(i)67 * 19
(iii)538 * 8
In each of the following numbers, replace * by the smallest number to make it divisible by 11:
(i)86 * 72
(ii)467 * 91
(iii)9 * 8071
Given an example of a number which is divisible by
(i)2 but not by 4
(ii)3 but not by 6
(iii)4 but not by 8
(iv)both 4 and 8 but not by 32
Which of the following statements are true?
(i)If a number is divisible by 3, it must be divisible by 9.
(ii)If a number is divisible by 9, it must be divisible by 3.
(iii)If a number is divisible by 4, it must be divisible by 8.
(iv)If a number is divisible by 8, it must be divisible by 4.
(v)A number is divisible by 18, if it is divisible by both 3 and 6.
(vi)If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii)If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii)If a number divides three numbers exactly, it must divide their sum exactly.
(ix)If two numbers are co-prime, at least one of them must be a prime number.
(x)The sum of two consecutive odd numbers is always divisible by 4.
Determine the HCF of the following numbers by using Euclid’s algorithm (i – x):
What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3respectively?
The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Determinethe longest rod which can measure the three dimensions of the room exactly.
A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones ofthe same size. Find the least possible number of such stones.
Determine the longest tape which can be used to measure exactly the lengths 7m, 3m 85cm and 12m95cm.
7.105 goats, 140 donkeys and 175 cows have to be taken across a river. There is only one boat which willhave to make many trips in order to do so. The lazy boatman has his own conditions for transporting them.He insists that he will take the same number of animals in every trip and they have to be of the same kind.He will naturally like to take the largest possible number each time. Can you tell how many animals wentin each trip?
Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equalnumber of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?
During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If youwant full packs of both and the same number of pencils and crayons, how many of each would you need tobuy?
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