find the hcf of : 12,15 2,6 7,18 24,48 with solution.
Answers
Answer:
Let us consider an example.
Find the H.C.F. of 24, 36 and 48.
First we find the prime factors of 24, 36 and 48.
Method of H.C.F.
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
The common prime factors = 2, 2, 3
H.C.F. = 2 × 2 × 3 = 12
3. H.C.F. by division method
Let us consider a few examples.
1. Find the H.C.F. of 12 and 18.
H.C.F. by Division Method
Step I: Treat the smallest number i.e., 12 as divisor and the bigger number i.e., 18 as dividend.
Step II: The remainder 6 becomes the divisor and the divisor 12 becomes the dividend.
Step III: Repeat this process till the remainder becomes zero. The last divisor is the H.C.F.
2. Find the H.C.F. of 16, 18 and 24.
Highest Common Factor by Division Method
Step I: First we consider the first two numbers and follow the same step 1, 2 and 3 of the above example.
Step II: The H.C.F. of the first two numbers which is 2 becomes the divisor and the third number 24 becomes the dividend. This process is repeated till the remainder becomes 0. H.C.F. is the last divisor.
3. Find the HCF of 18 and 54 by short division method.
Solution:
Write the number in a row separated by commas, divide the numbers by common prime factors. Factorisation stops when we reach prime numbers which cannot be further divided.
HCF is the product of all the common factors.
HCF by Short Division Method
0Save
Hence, the common factors are 2, 3 and 3.
HCF of 18 and 54 = 2 × 3 × 3 = 18.
4. Find the HCF of 28 and 36 by short division method.
Solution:
First we need to write the number in a row separated by commas, divide the numbers by common prime factors. Factorisation stops when we reach prime numbers which cannot be further divided.
HCF is the product of all the common factors.
HCF of 28 and 36 by Short Division Method
0Save
Hence, the common factors are 2, 2.
HCF of 28 and 36 = 2 × 2 = 4.
The factors of 2 are: 1, 2
The factors of 6 are: 1, 2, 3, 6
The factors of 7 are: 1, 7
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 15 are: 1, 3, 5, 15
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then the greatest common factor is 1.
Hope it helps!!