# Find Factors and Multiples of Whole Numbers - Grade 6

Examples and questions on how to find factors and multiples of whole numbers , with detailed solutions and explanations, for grade 6 students are presented.
Division and multiplication are related operations. The division 6 ÷ 3 = 2 (with remainder equal to 0) may be written as the multiplication: 6 = 2 × 3 The division 15 ÷ 3 = 5 (with remainder equal to 0) may be written as the multiplication: 15 = 5 × 3 The multiplication: 10 = 2 × 5 may be written as the division: 10 ÷ 5 = 2 (with remainder equal to 0) The multiplication: 18 = 6 × 3 may be written as the division: 18 ÷ 3 = 6 (with remainder equal to 0)
Examples 1) 6 = 1 × 6 ; 6 = 2 × 3 1, 2, 3 and 6 are called factors of 6. 2) 12 = 12 ×1 = 3 × 4 = 6 ×2 1, 2, 3, 4, 6 and 12 are called factors of 12. 3) 20 = 1 × 20 = 2 × 10 = 2 × 2 × 5 = 4 × 5 1, 2, 3, 4, 5, 10 and 20 are called factors of 20.
Examples Find all factors of 30 Divide 30 by all numbers starting from 1 and select the division that gives a remainder equal to 0 then write the factors. 30 ÷ 1 = 30 remainder 0 or 30 = 30 × 1. Hence 1 and 30 are factors 30 ÷ 2 = 15 remainder 0 or 30 = 15 × 2 . Hence both 2 and 15 are factors 30 ÷ 3 = 10 remainder 0 or 30 = 10 × 3 . Hence both 3 and 10 are factors 30 ÷ 4 = 7 remainder 2 , 4 is not a factor 30 ÷ 5 = 6 remainder 0 or 30 = 6 × 5 . Hence both 5 and 6 area factors. We stop here because all factors greater that 5 have already been found. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Take a whole number and multiply it by 1, 2, 3, 4, ... to obtain the multiples as follows: 5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 The results of the multiplication of 5 by 1, 2, 3, 4, ... which are 5, 10, 15, 20, ... are called the multiples of 5. |

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