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How many lines can pass through (a) one given point? (b) two given points?

(a) N number of countless lines can pass through a given point. (b) Only one line can pass through a two given points.... View Article

Use the figure to name: (a) Line containing point E. (b) Line passing through A. (c) Line on which O lies (d) Two pairs of intersecting lines.

Solution: (a) Line containing point E is (b) Line passing through A is (c) Line on which O lies is (d) Two pairs of... View Article

Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Solution The lines are , , , , , , , , , , , ... View Article

Use the figure to name: (a) Five points (b) A line (c) Four rays (d) Five line segments

Solution (a) The five points are D, E, O, B and C (b) A line is (c) Four rays are (d) Five... View Article

HCF of co-prime numbers 4 and 15 was found as follows by factorisation: 4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?

No. The answer is not correct. The correct answer is 1. Explanation Factors of 4 are 1, 2, 4. Factors of 15 are 1, 3, 5, 15. The common... View Article

What is the HCF of two consecutive (a) numbers? (b) even numbers? (c) odd numbers?

Highest Common Factor is the largest common divisor or gcd of two or more positive integers, as the mathematics rules dictate, appears to be the... View Article

If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. (True or False)

The given statement is False 2 divides 14 but it does not divide 9 and 5... View Article

If a number exactly divides two numbers separately, it must exactly divide their sum. (True or False)

The given statement is True 2 divides 6 and 2 and it also divides 8 (6 + 2 = 8)... View Article

All numbers which are divisible by 8 must also be divisible by 4. (True or False)

The given statement is True 2 × 4 = 8. Hence, if a number is divisible by 8, it will also be divisible by 2 and 4... View Article

All numbers which are divisible by 4 must also be divisible by 8. (True or False)

The given statement is False 36 is divisible by 4 but is not divisible by 8... View Article

If two numbers are co-primes, at least one of them must be prime. (True or False)

The given statement is False Since 15 and 32 are co-primes and also composite numbers... View Article

If a number is divisible by 9 and 10 both, then it must be divisible by 90. (True or False)

The given statement is True 9 × 10 = 90. Hence, if a number is divisible by both 9 and 10 then it is divisible by 90... View Article

A number is divisible by 18, if it is divisible by both 3 and 6. (True or False)

The given statement is False Since 24 is divisible by both 3 and 6 but is not divisible by 18... View Article

If a number is divisible by 9, it must be divisible by 3. (True or False)

The given statement is True 9 = 3 × 3. Hence, if a number is divisible by 9, it will also be divisible by 3... View Article

If a number is divisible by 3, it must be divisible by 9. (True or False)

The given statement is False For example 12 is divisible by 3 but is not divisible by 9... View Article

Find the common factors of: (a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120

(a) 20 and 28 Answer Factors of 20=1, 2, 4, 5, 10 and 20 Factors of 28= 1, 2, 4, 7, 14 and 28 Common factors of 20 and 28 are = 1, 2, 4... View Article

Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3: (a) 6724 (b) 4765 2

(a) __ 6724 Let us first add the digits of the given number 6+ 7+ 4+ 2=19 We know that The sum of its digit should be divisible by... View Article

Using divisibility tests, determine which of the following numbers are divisible by 11: (a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001 (f) 901153

Solution (a) 5445 Let us carry out the sum of the digits at odd places = 5 + 4 = 9 Let us carry out the sum of the digits at even places... View Article

Using divisibility tests, determine which of following numbers are divisible by 6: (a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852

(a) 297144 As the given number ends with 4. Hence, the last digit is divisible by 2 On adding all the digits of the given number, we... View Article

Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):

Numbers Divisible By 2 3 4 5 6 8 9 10 11 128 Yes No Yes No No Yes No No No 990 ------ ------ ------ ------ ------ ------ ------... View Article