Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Combine the factors, eliminating duplicates.
2 x 3 x 5 x 7 = 210, the LCM
Check it.
30 x 42 = 1260
210 x 6 = 1260
It checks.
As a product of its prime factors: 2*5*7 = 70 Note that at least two or more numbers are needed to find their HCF
In finding the LCM or HCF of two or more numbers
do the prime factorization of the 3 numbers. list the prime factors of all the 3 numbers. circle the factors that are common to the 3. multiply them. that number is the HCF
1
hcf(10, 21) = 1 ⇒ 10 & 21 relatively prime hcf(12, 54) = 6 ⇒ 12 & 54 not relatively prime hcf(15, 27) = 3 ⇒ 15 & 27 not relatively prime hcf(21, 38) = 1 ⇒ 21 & 38 relatively prime
As a product of its prime factors: 2*5*7 = 70 Note that at least two or more numbers are needed to find their HCF
In finding the LCM or HCF of two or more numbers
This is the way to do it.. Factorize 4,28 using prime numbers only (Prime factorization) till you get 1,1. The prime numbers used are 2,2 & 7 Therefore HCF(4,28)= 2*2*7 = 28.
Prime factorization is one of the ways you find the HCF.
22 x 33 is the prime factorization of 108. If you have another prime factorization, we can find a GCF and an LCM between the two.
The GCF is 6.
The prime factorization of 189 is 3 x 3 x 3 x 7. You need at least two numbers to find a GCF.
Each HCF has its own set of prime factors.
To find the HCF of two numbers you first need to break them down into their prime factors. In this case we get: 36 = 2x2x3x3 48 = 2x2x2x2x3 The next step is to identify any common prime factors. In this case, both numbers have two 2s and a 3 as prime factors. Multiply these together and you get 12. Therefore, the HCF of 36 and 48 is 12.
hcf(18, 54, 81) = 9. Using prime factorization: 18 = 2 x 3^2 54 = 2 x 3^3 81 = 3^4 hcf = 3^2 = 9
Prime factors of 36 are: 2^2 and 3^2 Prime factors of 144 are: 2^4 and 3^2 Prime factors common to both number are 2^2 and 3^2 which when multiplied equals 36 making it the HCF
To find the highest common factor (HCF) of 30, 210, and 700, you can use the prime factorization method. Prime Factorization: Prime factorize each number: 30 = 2 * 3 * 5 210 = 2 * 3 * 5 * 7 700 = 2^2 * 5^2 * 7 Identify Common Prime Factors: Identify the common prime factors among the numbers: 2, 3, 5, and 7. Multiply Common Prime Factors: Multiply the common prime factors: 2 * 3 * 5 * 7 = 210 Therefore, the HCF of 30, 210, and 700 is 210.