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Factoriszations - Word problems

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A factor is a number that divides another number exactly, leaving a remainder of 00.

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In word problems, if we need to divide things into equal groups or find the 'greatest' possible size, we look for common factors and the Highest Common Factor (HCF).

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If a word problem asks for something that repeats or the 'least' number/time when events happen together, we look for the Least Common Multiple (LCM).

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Every number (except 11) has at least two factors: 11 and the number itself.

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Common factors are factors that are the same for two or more numbers.

📐Formulae

Product=Factor1×Factor2\text{Product} = \text{Factor}_1 \times \text{Factor}_2

Dividend=Divisor×Quotient+0 (for factors)\text{Dividend} = \text{Divisor} \times \text{Quotient} + 0 \text{ (for factors)}

💡Examples

Problem 1:

A baker has 1212 vanilla cupcakes and 1818 chocolate cupcakes. He wants to pack them into boxes such that each box has the same number of cupcakes and only one type of cupcake. What is the greatest number of cupcakes he can put in each box?

Solution:

To find the greatest number of cupcakes per box, we need to find the Highest Common Factor (HCF) of 1212 and 1818. Factors of 1212: 1,2,3,4,6,121, 2, 3, 4, 6, 12 Factors of 1818: 1,2,3,6,9,181, 2, 3, 6, 9, 18 Common factors: 1,2,3,61, 2, 3, 6 The greatest common factor is 66.

Explanation:

Since the baker needs to pack the cupcakes into 'equal' groups and wants the 'greatest' number per box, we calculate the HCF of 1212 and 1818. The number 66 is the largest number that divides both 1212 and 1818 without a remainder.

Problem 2:

Riya wants to arrange 2424 chairs in her classroom in equal rows. List all the possible ways (number of rows and chairs per row) she can arrange them.

Solution:

We need to find all the factor pairs of 2424. 1×24=241 \times 24 = 24 (11 row of 2424 or 2424 rows of 11) 2×12=242 \times 12 = 24 (22 rows of 1212 or 1212 rows of 22) 3×8=243 \times 8 = 24 (33 rows of 88 or 88 rows of 33) 4×6=244 \times 6 = 24 (44 rows of 66 or 66 rows of 44) The possible factors are: 1,2,3,4,6,8,12,241, 2, 3, 4, 6, 8, 12, 24.

Explanation:

Any pair of numbers that multiplies to give 2424 represents a possible arrangement of rows and chairs. These pairs are called factor pairs.

Problem 3:

Two neon lights flash at different intervals. One flashes every 44 seconds and the other every 66 seconds. If they flash together now, after how many seconds will they next flash together?

Solution:

We need to find the Least Common Multiple (LCM) of 44 and 66. Multiples of 44: 4,8,12,16,20,24,…4, 8, 12, 16, 20, 24, \dots Multiples of 66: 6,12,18,24,30,…6, 12, 18, 24, 30, \dots The smallest common multiple is 1212.

Explanation:

When we want to find out when two events happening at different intervals will coincide again, we find the LCM. The first number that appears in both lists of multiples is 1212.