Page 68 - ICSE Math 6

4. Find the smallest number which is exactly divisible by 48, 36 and 72.

5. Find the smallest number which when divided by 24, 36, 54 and 60 leaves 4 as the remainder in
each case.

6. The HCF and LCM of two numbers are 5 and 385 respectively. If one of the two numbers is 55,
find the other number.
7. Find the LCM of 27 and 90. Use the LCM to find their HCF.

8. The HCF of 13 and 169 is 13, find their LCM.

AT A GLANCE

¾ A factor of a given number is a number which divides the given number completely.
¾ A multiple of a number is obtained by multiplying the given number by a natural number.
¾ An even number is divisible by 2, and an odd number is not divisible by 2.

¾ Any natural number (greater than 1) which is divisible only by 1 and itself is known as a prime
number.

¾ Any number which has at least one factor other than 1 and itself is known as a composite number.
¾ If the digit at ones place of a number is either 0 or an even number, then the number is divisible
by 2.
¾ If the sum of all the digits of a number is divisible by 3, then the number is divisible by 3.

¾ If the number formed by the last two digits of a given number is divisible by 4, then the given
number is divisible by 4.

¾ If the digit at ones place of a number is either 0 or 5, then the number is divisible by 5.
¾ If a number is divisible by both 2 and 3, then the number is divisible by 6.
¾ If the number formed by the last three digits of a given number is divisible by 8, then the given
number is divisible by 8.
¾ If the sum of all the digits of a number is divisible by 9, then the number is divisible by 9.
¾ If the digit at ones place of a number is 0, then the number is divisible by 10.

¾ If the difference between the sum of the digits at the odd places and the sum of the digits at the
even places is either zero or a multiple of 11, then the number is divisible by 11.

¾ Two numbers which do not have a common factor other than 1 are known as co-prime numbers.
¾ Highest common factor (HCF) of two or more numbers is the largest factor which divides each
given number completely.
¾ LCM of two or more numbers is the smallest multiple from the common multiples of the given
numbers.
¾ For any two numbers, HCF × LCM = Product of the two numbers.

MENTAL MATHS

1. Write True or False.
(a) 2 is a factor of 12. (b) 3 is a factor of 10.

(c) 5 is a factor of 75. (d) 7 is a factor of 17.

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