Download 2016-17 Factors and Multiples

L. R. & S. M. VISSANJI ACADEMY
SECONDARY SECTION - 2016-17
MATHEMATICS-GRADE: VII
Factors and Multiples
Keywords: Factors, multiples, co-primes, prime triplets, perfect numbers, prime
factorization, Sieve of Eratosthenes.
 If ab=c, where a,b,c belongs to N then a and b are called factors of c. The product c is called
multiple of a and b.
 A natural number greater than 1, which has exactly two factors, namely 1 and itself, is called
a prime number.
 A natural number having at least one factor, besides 1 and itself is called a composite
number.
 The number 1 has only one factor, so it’s neither prime nor composite.
 Two consecutive odd prime numbers are known as twin numbers.
 Two numbers are said to be co-prime if they do not have a common factor other than 1.
 Two prime numbers are always co-prime.
 If two numbers are given, then
Product of two numbers = Product of their H.C.F and L.C.M
 The H.C.F of given numbers is always a factor of their L.C.M.
 A number is divisible by:
 2 - if the unit digit is 0,2,4,6 or 8.
 3 - if the sum of digits is exactly divisible by 3.
 4 - if the last two(tens and unit digit ) digits of a number are zero or exactly divisible by 4.
 5 - if the unit digit is 0 or 5.
 6 - if the number is divisible by 2 and 3.
 7 - if the difference between the sums of digits in alternate places of three digits from right
to left is divisible by 7.
 8 - if the last three digits from a number is divisible by 8.
 9 - if the sum of the digits is divisible by 9.
 10 - if the last digit is 0.
 11- if the difference of the sums of digits at the alternate places is divisible by 11.
Extra questions
1. Find the H.C.F and L.C.M of 684 and 1197.
2. Test whether 2275 is divisible by 7.
3. Test whether 297144 is divisible by 6.
4. Find the L.C.M of 105,135 and 180 by prime factorization method.
5. Find the H.C.F and L.C.M of two numbers which are 89 and 1335 respectively. If one of the
numbers is 267, find the other.
6. The H.C.F of two numbers is 16 and their product is 3072.Find their L.C.M.
7. The H.C.F of two numbers is 23 and their L.C.M is 1449.If one of the numbers is 161, find the
other.
Answers:
1. H.C.F=171, L.C.M=4778
2. Yes, it is divisible by 7.
3. Yes, it is divisible by 6.
4. L.C.M=3780.
5. Other number: 445
6. L.C.M=192
7. Other number:207