Test

• The number 792 written as the product of it's prime factors is "792= 2(3) x 3(2) x 11"

  i ) Write 540 as the product of it's prime factors

  ii ) Hence, find the HCF and LCM of 540 and 792

  Ans :

  i ) 2(2) x 3(3) x 5

  ii ) HCF = 36 LCM = 11880
• i ) Given that 2(6) x 11(2) = 7744, evaluate square root of 7744

  ii ) Write 1728 as the product of it's prime factors in index notation. Hence, find the value of the cube root of 1728

  Ans:

  i ) 88

  ii ) 2(6) x 3(3), 12
• i ) Show 50 x 98 is a perfect square

  ii ) A number has exactly 8 factors. 2 of the factors are 27 and 45. List al the factors of the number

  Ans:

  i ) Since all prime factors have powers of 2, 50 x 98 is a perfect square

  ii ) 1 , 3, 5, 9, 15, 27, 45, 135
• i ) Explain whether each of the following numbers is prime of composite

  191, 161

  ii ) - Express 4225 as the product of its prime factors in index notation

  -Hence fund square root of 42,250,000 using prime factorization

  Ans:

  i ) 191 - Prime number. Since 191 is not divisibly by any prime numbers, 191 is a prime number.

  161 - Composite number. Since 161 is divisible by 7, then 161 is a composite number.

  ii )

  • 4225 = 5(2) x 13(2)
  • 6500
• i ) Express 2916 as the product of its prime factors in index notation

  ii ) Hence, use your result from part i ) to find the cube root of 5832

  Ans:

  i ) 2(2)x 3(6)

  ii ) 18
• i ) Express 1936 as a product of its prime factors

  Ans ; 1936 = 2(4) x 11(2)

  ii ) Using your answer to part ( i ), explain why 1936 is a perfect square

  Ans ; Since 1936 = [2(2) x 11(2)], it is a perfect square

  iii ) a and b are both prime numbers. Find the values of a and b such that 1936 x a/b is a perfect cube

  Ans ;

  a = 11

  b = 2
• Given that m = 3(3) x 5(2) x 7 and n = 2 x 3(2) x 5(3) x 11, find the HCF and the LCM of m and n, giving your answer in index notation.

  Ans

  HCF = 3(2) x 5(2)

  LCM = 2 x 3(3) x 5(3) x 7 x 11
• the product of the prime factors of three numbers are given below.

  240 = 2(4) x 3 x 5

  756 = 2(2) x 3(3) x 7

  3168 = 2(5) x 3(2) x 11

  Find

  i ) the HCF of 240, 756 and 3168

  ii ) the LCM of 240 756 and 3168

  iii ) the smallest positive integer k such that 3168k is a perfect cube

  Ans

  i ) HCF = 2(2) x 3 = 12

  ii ) LCM = 2(5) x 3(3) x 5 x 7 x 11 = 3332640

  iii ) Smallest integer value of k = 2 x 3 x 11(2) = 726
• i ) Express 300 as the product of its prime factors

  ii ) Find two numbers, both less than 100, that have a lowest common multiple of 300 and a highest common factor of 15

  Ans

  i ) 300 = 2(2) x 3 x 5(2)

  ii ) First number = 2(2) x 3 x 5 = 60, Second number = 3 x 5(2) = 75
• i ) Find the smallest possible integer which can be divided by 2, 5, 6, 8.

  ii ) Find the largest prime factor of 1368.

  Ans

  i ) The smallest possible integer that can be divided by 2, 5, 6, and 8 is 120

  ii ) Largest prime number = 19
• i ) Find the product of HCF and the LCM of 24, 45 and 75.

  ii ) The lowest common multiple of 10, 15 and p is 150. Find the two possible values of p which are odd numbers

  Ans

  i ) 5400

  ii ) p = 5(2) = 25 / p = 3 x 5(2) = 75
• i ) Express 2880 as the product of its prime factors in index notation.

  ii ) Hence, find

  a : the smallest positive integer R such that the product of 2880R is a perfect square

  b : the smallest positive integer S such that the product of 2880S is a perfect cube

  Ans

  i ) 2880 = 2(6) x 3(2) x 5

  ii ) a : R = 5 b : S = 75
• i ) Express 3969 and 9261 as the products of their prime factors in index notation.

  ii ) Hence find :

  a ; the positive square root 3969

  b ; the cube root of 9261

  c ; the largest integer is a factor of both 3969 and 9261

  Ans

  i ) 3969 = 3(4) x 7(2) 9261 = 3(3) x 7(3)

  ii )

  a ; 63

  b ; 21

  c ; The largest integer that is a factor of both 3969 and 9261 is 1323
• i ) Express 7056 as the product of its prime factors in index notation

  ii ) Hence, evaluate square root of 7056, expressing your answer in index notation.

  iii ) Given that 180 = 2(2) x 3(2) x 5, find the smallest integer value k such that 7056k is a multiple of 180

  Ans

  i ) 7056 = 2(4) x 3(2) x 7(2)

  ii ) square root 7056 = 2(2) x 3 x 7

  iii ) k = 5