(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90
(a) If two numbers are co primes, at least one of them must be prine,
(All numbers which are divisible by 4 must also be divisible by
Id All numbers which are divisible by a must also be divisible by 4
(h) If a number exactly divides two numbers separately, it must exactly divide their sum,
() If a number exactly divides the sum of two numbers, it must exactly divide the two numbers
separately
Write the numbers which are neither prime nor composite. How many such number are there!
Using each of the digits 1, 2, 3 and 4 only once determine the smallest four digit number wisible by
Write the greatest 4-digit number and express it in terms of its prime factors,
Find the largest three-digit number exactly divisible by 3, 6 and 8
The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and
08 seconds respectively. If they change simultaneously at 7 am, at what time will they change
imultaneously again?
ind the least number which when divided by 6, 15 and 18 leave remainder 5 in each case,
nd the smallest 4-digit number which is divisible by 18,24 and 32
ne product of three consecutive numbers is always divisible by 6. Verify this statement with the help
some examples
up the factor tree using prime number:
40
72.
32
199
2
2
2
tag
199
Answers
Answer:
1. False 2. True 3. False 4. True 5. False 6. False 7. False 8. True 9. False
Explanation:
(a) If a number is divisible by 3, it must be divisible by 9.
False. We can prove it with the help of an example. 12 is divisible by 3 but it is not divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
True. If a given number is divisible by some number then it is also divisible by its factor.
(c) A number is divisible by 18, if it is divisible by both 3 and 6.
False. 12 is divisible by both 3 and 6 but it is not divisible by 18.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
True. This is because if a number is divisible by two given co-prime numbers then it is also divisible by their product. We know that 9 and 10 are co-primes and their product is equal to 90.
(e) If two numbers are co-primes, at least one of them must be prime.
False. Take an example, 8 and 9 are co-prime numbers and none of them is a prime number.
(f) All numbers which are divisible by 4 must also be divisible by 8.
False. 12 is divisible by 4 but it is not divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
True. If a number is divisible by another number then it is divisible by each of the factors of that number.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
True. Take different examples and check this property.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
False. Let's take an example, 9 and 3 are not divisible by 4 but their sum is divisible by 4.