Lesson Notes By Weeks and Term v3 - Junior Secondary 1
HCF
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HCF
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Subject: General Mathematics
Class: Junior Secondary 1
Term: 1st Term
Week: 3
Theme: Number And Numeration
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Identify common factors of whole number Find the HCF of whole numbers; Identify the difference between LCM and HCF; Solve problems on quantitative aptitude in volving LCM and HCF whole numbers
A factor of a whole number is any whole number that divides the given number exactly, resulting in a zero remainder. Every whole number greater than 1 has at least two factors: 1 and itself.
Example 1: Finding factors of 20 To find the factors of 20, consider all pairs of whole numbers that multiply to give 20: $1 \times 20 = 20$ $2 \times 10 = 20$ $4 \times 5 = 20$ The factors of 20 are 1, 2, 4, 5, 10, and
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0. A factor of a whole number is a number that divides it exactly, without leaving a remainder.
Example 1: Factors of 12 are numbers that divide 12 exactly. $12 \div 1 = 12$ $12 \div 2 = 6$ $12 \div 3 = 4$ $12 \div 4 = 3$ $12 \div 6 = 2$ $12 \div 12 = 1$ Therefore, the factors of 12 are 1, 2, 3, 4, 6, and
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2. Common factors of two or more whole numbers are the factors that are shared by all the numbers.
Example 2: Find the common factors of 18 and
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4. Factors of 18: {1, 2, 3, 6, 9, 18} Factors of 24: {1, 2, 3, 4, 6, 8, 12, 24} By comparing the lists, the common factors are the numbers present in both sets: {1, 2, 3, 6}. Common factors are factors that two or more whole numbers share. To identify common factors, list the factors for each number and then select the ones that appear in all lists.
Example 2: Finding common factors of 12 and 18 Factors of 12: {1, 2, 3, 4, 6, 12} Factors of 18: {1, 2, 3, 6, 9, 18} By comparing the two sets of factors, the numbers that appear in both lists are 1, 2, 3, and
6. Therefore, the common factors of 12 and 18 are 1, 2, 3, and 6.
Market Stalls and Product Display: A trader at Onitsha Main Market receives two batches of soft drinks: 72 bottles of Coke and 96 bottles of Fanta. To create an attractive display, the trader wants to arrange them in rows with an equal number of bottles in each row, ensuring no mixed rows and no bottles are left out. To find the largest possible number of bottles per row, the trader would calculate the HCF of 72 and 96. (HCF(72, 96) = 24). This ensures maximum uniformity and efficiency in space usage.
Community Sanitation Project: In a community health initiative, 105 volunteers are available for street cleaning and 140 volunteers for drainage clearing. The project coordinator wants to form identical teams for both tasks, with each team having the same number of members and no volunteers left over. To find the largest number of teams that can be formed, the HCF of 105 and 140 would be used. (HCF(105, 140) = 35). This helps in optimal resource (manpower) allocation.
School Resource Distribution: A school receives 160 exercise books and 200 pens as a donation. The headteacher wants to distribute these to students in identical packages, with each package containing the same number of exercise books and pens, and no items remaining. To determine the maximum number of students who can receive such packages, the HCF of 160 and 200 is needed. (HCF(160, 200) = 40). This ensures fair and equitable distribution among the largest possible number of beneficiaries.