2013 MTAP DepEd Saturday Mathematics Program Grade 5 Session 3 TG

This session covers Number Theory. It includes the required learning competencies specified below.

1. Divisibility2. Factors and multiplies of given numbers3. List the prime factors of given numbers4. Writes the prime factorization of a given number5. Determines the greatest common factor (GCF) of 2 or more numbers6. Determines the least common multiple (LCM) of 2 or more numbers

I. A. Without actually dividing, put a check in the corresponding box if the given number in the first column is divisible by the number at the top.

Number 2 3 4 5 6 7 8 9 10 1123 600 / / / / /63 372 / / / /81 432 / / / / / /

214 890 / / / / /1 161 914 /

B. 1) 0,2,4,6,8 2) 2,5,8 3) 2,6 4) 0,5 5) 2,8 6) 5 7) 8 8) 2

II. A) 1) 6= 2,3 2) 15 = 5,3 3) 15; 15 = 5,3 4) 12 = 3, 4;4 = 2,2

B) 1) 3 x 5 2) 2 x 13 3) 22 x 11 4) 32 x 7 5) 3 x 5 x 7

6) 22 x 7 5 7) 2 x 3 52 8) 2 x 7 x 13 9) 2 x 5 x 112 10) 7 x 323

III A) 1) 4 2) 6 3) 2 4) 3 5) 1 6) 18 7) 21 8) 12 9) 2 10) 4 11) 4 12) 9 13) 8 14) 13 15) 2 B) 1) 12 2) 112 3) 48 4) 48 5) 36 6) 90 7) 15 8) 273 9) 144 10) 60 11) 80 12) 90 13) 240 14) 72 15) 2 205

IV. 1. A) 105 b) 108, 117, 126, 135, 144, 153, 162, 171 Answer: 8

2.) 2, 4, 5, 8, 10, 20, 40 9.) 2cm3. 22 x 3 x 5 = 60 10.) 614.) 23 x 33 x 5 = 8 x 9 = 360 11.) 125.) 180 13.) 1446) A + B = 8 14.) 7m 2 556, 4 554, 6 552, 8 550 15) 6, 8, 10, 14, 22, 26

7.) 6 groups maybe formed each with 4 sopranos, 10 altos and 6 tenors 3 groups maybe formed each with 8 sopranos, 20 altos and 12 tenors 2 groups maybe formed each with 12 sopranos, 30 altos and 18 tenors

Challenge1. 180 and 12; 36 and 60 2. 1193. The numbers divisible by 11 are: 1 749, 1 947, 4 719, 7 194, 7 491, 9 174, 9 1474. 587 and 25. The ones digits of the numbers divisible by 8 has a pattern 0, 8, 6, 4, 2. The ones digit repeat every 5

multiplies of 8. Thus, there are 1 000 / (8 x 5) = 25 pages that have the digit 2 in the ones place and are divisible by 8.

2013 MTAP DepEd Saturday Mathematics Program Grade 5 Session 3 TG

I. A. Without actually dividing, put a check in the corresponding box if the given number in the first column is divisible by the number at the top.

Number 2 3 4 5 6 7 8 9 10 1123 60063 37281 432

214 8901 161 914

B. In 247__, what digit should be in the __ so that the number is divisible by 1) 2 2) 3 3) 4 4) 5 5) 6 6) 9 7) 10 8) 12

C. Determine all values of the digit “d” such that the number formed is divisible by the number on its right.1) 4d2; 3 2) 8d37; 9 3) d70 ; 9 4) 614d ; 95) 3 0d2 ; 6) 52 31d ; 15 7) 314 67d ; 9 8) 117 4d2 ; 18

II A. Supply the missing number in each factor tree

1. 24 2. 45

3. 75 4. 24

B. Express the following as a product of prime factors. Use exponents when applicable

1)15 2) 26 3) 44 4) 63 5) 1056) 140 7) 150 8) 182 9) 1 210 10) 2 261

III A. Find the GCF of the following sets of numbers

1) 16, 44 2) 24, 6 3) 20, 26 4) 21, 395) 10, 21 6) 36, 54 7) 63, 84 8) 108, 1569) 140, 168 10) 132, 680 11) 20, 28, 40 12) 18, 36, 2713) 24, 40, 96 14) 104, 78, 117 15) 280, 324, 378

B. Find the LCM of the following sets of numbers

1) 4,6 2) 8, 112 3) 12, 16 4) 16, 245) 9, 12 6) 15, 18 7) 45, 75 8) 39, 919) 8, 16, 15 10) 10, 12 11) 16, 20 12) 18, 3013) 8, 16, 15 14) 12, 18, 24 15) 35, 45, 63

IV. Solve the following

1. a. What is the multiple of 7 nearest to but greater than 10? b. How many multiplies of 9 are there between 101 and 173?2. List all factors of 40.3. Find the GCF of 24 x 32 x 5 and 22 x 3 x 52

4. Find the LCM of 23 x 33 and 2 x 32 x 55. Ruth can arrange her stickers either 9 on the page, 12 on a page of 15 on a page. What is the smallest

number of stickers that will allow her to do this?6. The 4-digit number A55B is divisible by 18 without remainder. What is A+B? What numbers can A55B be?

7. Your music teacher wants to divide the school choir into smaller groups. There are 24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each type of voice. How many smaller groups can be formed? How many each sopranos, altos and tenors are there in the small group?

8. The greatest common factor of two number is 30. Their least common multiple is 420. One of the numbers is 210. What is the other number?

9. Jose has three pieces of rope with lengths of 140 cm, 168 cm and 230 cm. He wishes to cut the three pieces of rope in to smaller pieces of equal length with no remainders. What is the greatest possible length of each of the smaller pieces?

10. What is the greatest number by which 1037 and 1159 can both be divided exactly?11. The Division Supervisor wishes to distribute 84 balls and 180 bats equally among a number of schools. Find

the greatest number of schools receiving the items in this way.12. An ice cream bar producer puts a coupon for a free bar in every 80 th bar he produces, and a coupon for two

free bars in every 180th bar. How often does he put both coupons in a single bar? 13. If one car can travel 18 kilometers per liter of gasoline and another car can travel 16 kilometers per liter of

gasoline, what is the smallest natural number of liters of gasoline each consumes if it travels exactly the same distance?14. Mr. Jones wishes to cut as many pieces of rope or equal length as he can from three strands that are 35

meters, 49 meters, and 56 meters long. If he wishes the pieces to be as long as possible and does not wish to waste any rope, how long should he cut each piece?

15. Find all the numbers from 1 to 30 that have 4 factors.

Challenge

1. The product of two numbers is 2 160 and their GCF is 12. Find all possible pairs of such numbers.2. What is the least multiple of 7 which when divided by 2, 3, 4, 5 and 6 leaves the remainders 1, 2, 3, 4, 5,

respectively?3. A four-digit number contains the digit 1, 4, 7 and 9 but not in that order. Arrange these digits so that the

number is divisible by 11. In how many ways can this be done?4. The sum of two different numbers that have two factors is 589. What are the two numbers?5. The pages of a book are numbered consecutively from 1 to 1 000. How many page numbers have the digit 2

in the ones place and are divisible by 8?