Grade DE Multiples and Factors Understand find multiples

Grade D/E Multiples and Factors Understand find multiples and factors If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Factor Multiple

How to find multiples of numbers • A multiple of a number is found by multiplying the number by any whole number. • To find the fist five multiples of 5 multiply 5 by 1, 2, 3, 4, 5. . . Working Out 5 x 1 Multiples 5 of 5 5 x 2 5 x 3 5 x 4 5 x 5 10 15 20 25

How to find factors of a number A factor is a whole number that whole number. Factors come in pairs. Does three go into 40? No so now try 4. . into divides exactly a To find the Factors of 40 we list the numbers Doesthat 6 go into 40? Does 7 go into 40? divide into 40 exactly : 1 2 4 5 8 10 20 40

How to find the LCM ‘Listing method’ By ‘Lowest Common Multiple’ we mean the lowest multiple of two or more numbers that is common to each of the numbers. Find the LCM of 4 and 6 First list the multiples of each number Multiples of 4= 4, 8, 12, 16, 20, 24, …. Multiples of 6= 6, 12, 18, 24, 30, 36, … Scan both rows of multiples and find the lowest multiple that is common to both numbers, so the LCM of 4 and 6 is… 12

How to find the HCF ‘Listing method’. . . Highest Common Factor (HCF)- The highest number that goes into two given numbers. Find the HCF of 36 and 56 36 = 1, 2, 3, 4, 6 9, 18, 36 56 - 1, 2, 4, 7, 8, 14, 28, 56 Search for the common factors and pick the highest one! HCF = 4

Find the HCF and LCM now you try. . . Find the HCF of 6 and 18 Find the HCF of 25 and 35 Find the HCF of 35 and 70 Find the LCM of 9 and 4 Find the LCM of 4 and 16 Find the LCM of 6 and 7

Find the HCF and LCM now you try. . . Find the HCF of 6 and 18 Find the HCF of 25 and 35 Find the HCF of 35 and 70 6 5 7 Find the LCM of 9 and 4 Find the LCM of 4 and 16 Find the LCM of 6 and 7 36 16 42

How to spot when being asked to find the HCF A worded question may be asking for the HCF if you are asked: • to split things into smaller sections. • to equally distribute sets of items into the largest grouping possible. • to work out how many people to invite to something. • to arrange something into rows or groups.

How to answer a HCF worded question Debra has two sheets of card. One sheet is 81 inches wide and the other piece is 63 inches wide. She wants to cut both pieces into smaller strips of equal width that are as wide as possible. . How wide should she cut the strips? This suggests a HCF question! Find the HCF of 81 and 63 Factors of 63 = 1, 3, 7, 9, 21, 63 Factors of 81 = 1, 3, 9, 27, 81 The HCF is 9 so each width should be 9 cm long.

How to answer a worded LCM problem. . . An LCM question may ask you… • about an event that is or will be repeating… • to purchase several items in order to have enough. • to work out when something will occur again at the same time.

How to spot an LCM question. . . • Lighthouse A appears to flash every 15 seconds and Lighthouse B appears to flash every 6 seconds. How many times will each Lighthouse flash before they will flash at the same time? This suggests a HCF question List the multiples of 15 and 6 Light house A – 15, 30, 45, 60 Lighthouse B -6, 12, 18, 24, 30 Lighthouse A will flash twice and Lighthouse B will appear to flash 5 times. It will take 30 seconds for them to flash at the same time.

Problem Solving and Reasoning Louise is hosting a barbecue. She is going to buy packs of burgers and packs of sausages. Burgers are sold in packs of 8 and burgers in packs of 5. How many packs of each will she need to buy so that the number of burgers and sausages are equal? There are 24 boys and 32 girls at a youth group. In order to go on a trip the boys and girls must be put into smaller groups. If there are to be the same number of boys and girls in each group, what size should each group be?

Problem Solving and Reasoning Louise is hosting a barbecue. She is going to buy packs of burgers and packs of sausages. Burgers are sold in packs of 8 and burgers in packs of 5. How many packs of each will she need to buy so that the number of burgers and sausages are equal? 40 There are 24 boys and 32 girls at a youth group. In order to go on a trip the boys and girls must be put into smaller groups. If there are to be the same number of boys and girls in each group, what size should each group be? 8

Reasoning and explain What does it mean to say that an integer can have an infinite number of multiples? What is the difference between a factor and a multiple? How do you spot a worded HCF question? How do you spot a worded LCM question?