Lcm of two numbers is 256 and their hcf is 64. if one of the numbers is 64, the other number is:

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Last updated - May 06, 2022

Answer: HCF = 8 and LCM = 768

Step by step solution:

Contents:

Given numbers = 24 and 256

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 24:
24 = 2 × 12
= 2 × 2 × 6
= 2 × 2 × 2 × 3

Prime Factorization of 256:

HCF of 24 and 256 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 2, 2, 2

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

HCF = 2 × 2 × 2
= 8

∴ HCF(24, 256) = 8

LCM of 24 and 256 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
= 768

∴ LCM(24, 256) = 768

Division Method:

HCF of 24 and 256 by division method:

In the above division, the last divisor is 8.

Hence the HCF(GCF) of 24 and 256 = 8

∴ HCF(24, 256) = 8

LCM of 24 and 256 by division method

∴ LCM(24, 256) = 768

HCF of 24 and 256 by Listing Factors Method:

To find HCF by listing factors method we will list down all the factors of the given numbers.

Factors of 24:

1234681224

Factors of 256:

1248163264128256

The greatest common factor in the above lists will be the HCF of the given numbers.

8 is the greatest factor which is common in the above lists.

∴ HCF(24, 256) = 8

If the HCF of two numbers is 8 and their product is 6144, what is their LCM?

If the LCM of two numbers is 768 and their product is 6144, what is their HCF?

HCF and LCM of two numbers is 8 and 768 respectively. If one number is 24, what is the other number?

Let other number be x.
Given:
HCF(24, x) = 8
LCM(24, x) = 768
∵ HCF × LCM = product of numbers
∴ 8 × 768 = 24 × x
∴ 6144 = 24x
∴ 6144⁄24 = x
∴ x = 256
Hence, the other number is 256.

Last updated - May 01, 2022

Answer: HCF = 2 and LCM = 256

Step by step solution:

Contents:

Given numbers = 2 and 256

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 2:
2 = 2

Prime Factorization of 256:

HCF of 2 and 256 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 2

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

Here, 2 is the only common factor in the above prime factors.

∴ HCF(2, 256) = 2

LCM of 2 and 256 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 256

∴ LCM(2, 256) = 256

Division Method:

HCF of 2 and 256 by division method:

In the above division, the last divisor is 2.

Hence the HCF(GCF) of 2 and 256 = 2

∴ HCF(2, 256) = 2

LCM of 2 and 256 by division method

∴ LCM(2, 256) = 256

HCF of 2 and 256 by Listing Factors Method:

To find HCF by listing factors method we will list down all the factors of the given numbers.

Factors of 2:

12

Factors of 256:

1248163264128256

The greatest common factor in the above lists will be the HCF of the given numbers.

2 is the greatest factor which is common in the above lists.

∴ HCF(2, 256) = 2

If the HCF of two numbers is 2 and their product is 512, what is their LCM?

If the LCM of two numbers is 256 and their product is 512, what is their HCF?

HCF and LCM of two numbers is 2 and 256 respectively. If one number is 256, what is the other number?

Let other number be x.
Given:
HCF(256, x) = 2
LCM(256, x) = 256
∵ HCF × LCM = product of numbers
∴ 2 × 256 = 256 × x
∴ 512 = 256x
∴ 512⁄256 = x
∴ x = 2
Hence, the other number is 2.