maths

1. HCF AND LCM

2. PRIME FACTORIZATION
• It is the expression of a given number as theproduct of prime numbers.
• It can be done using factor tree method ordivision method.
• Fundamental Theorem of Arithmetic states that every composite number
has only one factorization.

3. FACTOR TREE METHOD
• Draw the factor tree and write down the prime factorisation of the
followingnumbers

4. PRIME FACTORIZATION THROUGH
DIVISION METHOD
STEPS
• Divide the number with a prime numberwhich will divide it
exactly.
• Continue dividing the quotient until you get aquotient which is a
prime number

5. HCF (HIGHEST COMMON FACTOR)
• Highest common factor (H.C.F) of two or more numbers is the greatest
number which divides each of them exactly. Thereare many methods to find
them.
1.listing the factors
2.HCF by Prime Factorization
3.HCF by Common division method
4. HCF by long division method.

6. FIND THE HCF OF FOLLOWING NUMBERS USINGTHE
METHOD OF LISTING FACTORS.
24,30
24- 1,2,3,4,6,8,12,24
30- 1,2,3,5,6,10,15,30
COMMON FACTORS OF 24 AND 30- 1,2,3,6
HIGHEST COMMON FACTOR- 6
24,72
24-1,2,3,4,6,8,12,24
72-1,2,3,4,8,9,18,24,36,72
COMMON FACTORS of 24and 72 are 1,2,3,4,8,24
Highest common factor- 24

7. Find the HCF of following numbers using themethod of
Prime factorization.
• Step 1: find the prime factors of givennumbers.
• Step 2:find the common factors and circlethem.
• Step 3 multiply the common factors.

8. 30,96
• Prime factorization of 30- 2x3x5
• Prime factorization of 96- 2x2x2x2x3x2
• Hcf -2x3= 6

9. LCM(LOWEST COMMON MULTIPLE)
• The lowest common multiple of two or more numbers is the lowest of
theircommon multiples.
• It is either equal to or greater than the numbers.
• The two methods to find LCM are
1. Prime Factorization
2. Common division

10. LCM THROUGH PRIME
FACTORIZATION
• Step 1- Do the prime factorization of all the numbers.
• Step 2- Express it in terms of powers.
• Step 3- Multiply the highest powers of each number.

11. FIND THE LCM USING PRIME
FACTORIZATION.
• 72,90
Prime Factorization of 72-2x2x2x3x3
= 2³x 3²
Prime Factorization of 90 - 2x5x3x3
= 2¹x 5¹x 3²
LCM of 72 and 90 = 2³x 3²x5¹
=2x2x2x3x3x5=360

12. • b) 16,30,42
Prime factorization of 16= 2x2x2x2=2⁴
Prime factorization of 30=2x3x5=2¹x3¹x5¹
prime factorization of 42= 2x3x7=2¹x3¹x7¹
lcm of 16,30 and 42 =2⁴x3¹x5¹x7¹
2x2x2x2x3x5x7
=4x4x15x7=16x105=1680

13. RELATIONSHIP BETWEEN HCF AND
LCM
• The product of two numbers is the product of their HCFand LCM.
• a x b= HCF x LCM
• a = HCF x LCM/b
• b = HCF x LCM/a
• HCF= a xb/LCM
• LCM= a xb/HCF

14. • The HCF of two numbers is 12 and their product is 4320. What is their
LCM? If one of thenumbers is 60, what is the other number?
HCF = 12
Ax B=4320
LCM= AXB/HCF = 4320/12 = 360
ONE NUMBER=60
THE OTHER NUMBER= 4320/60 =72
OR
B= HCF X LCM/A = 12X 360/60 = 4320/60 =72

15. • The HCF and LCM of two numbers is 15 and 450 respectively. If one
number is 75, whatis the other number?
HCF= 15
LCM= 450
A= 75
B= HCFX LCM/A =15X450/75 = 90

16. THANK YOU