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what is the largest number that divides each one of 1152 and 1664 exactly?

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What is the largest number that divides each one of 1152 and 1664 exactly ? a 32 b 64 c 128 d 256

What is the largest number that divides each one of 1152 and 1664 exactly ? a 32 b 64 c 128 d 256

Method of Finding HCF

What is the l... Question

What is the largest number that divides each one of 1152 and 1664 exactly ?

(a) 32 (b) 64 (c) 128 (d) 256

Open in App Solution

HCF of 1152 and 1164

1164=1152 × 1+512 1152=512 × 2+128 512=128 × 4+0 So, HCF is 128 Suggest Corrections 29 SIMILAR QUESTIONS

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स्रोत : byjus.com

What is the largest number that divides each one of 1152 and 1664 exactly?

Q.7 of chapter 1, 1. Real Numbers - RS Aggarwal - Mathematics book. What is the largest number that divides each one of 1152 and 1664 exactly?

Book: RS Aggarwal - Mathematics

Q. No. 7 of Multiple Choice Questions (MCQ)

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

7

What is the largest number that divides each one of 1152 and 1664 exactly?

The largest number that can divide both the numbers will be the HCF of the two numbers -

So prime factors of the numbers –

1152 = 27 × 32 1664 = 27 × 13.

∴ HCF of number = 27 = 128.

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स्रोत : philoid.com

HCF of 1152 and 1664

HCF of 1152 and 1664 is the largest possible number which divides 1152 and 1664 without leaving any remainder. The methods to compute the HCF of 1152, 1664 are explained here.

HCF of 1152 and 1664

HCF of 1152 and 1664 is the largest possible number that divides 1152 and 1664 exactly without any remainder. The factors of 1152 and 1664 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152 and 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 respectively. There are 3 commonly used methods to find the HCF of 1152 and 1664 - prime factorization, long division, and Euclidean algorithm.

What is HCF of 1152 and 1664?

Answer: HCF of 1152 and 1664 is 128.

Explanation:

The HCF of two non-zero integers, x(1152) and y(1664), is the highest positive integer m(128) that divides both x(1152) and y(1664) without any remainder.

Methods to Find HCF of 1152 and 1664

Let's look at the different methods for finding the HCF of 1152 and 1664.

Listing Common Factors

Prime Factorization Method

Long Division Method

HCF of 1152 and 1664 by Listing Common Factors

Factors of 1152: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152Factors of 1664: 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664

There are 8 common factors of 1152 and 1664, that are 32, 1, 2, 64, 4, 128, 8, and 16. Therefore, the highest common factor of 1152 and 1664 is 128.

HCF of 1152 and 1664 by Prime Factorization

Prime factorization of 1152 and 1664 is (2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 2 × 2 × 2 × 13) respectively. As visible, 1152 and 1664 have common prime factors. Hence, the HCF of 1152 and 1664 is 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128.

HCF of 1152 and 1664 by Long Division

HCF of 1152 and 1664 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1664 (larger number) by 1152 (smaller number).Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (1152) by the remainder (512).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (128) is the HCF of 1152 and 1664.

☛ Also Check:

HCF of 10 and 15 = 5

HCF of 3 and 9 = 3 HCF of 7 and 9 = 1

HCF of 441, 567 and 693 = 63

HCF of 12 and 16 = 4

HCF of 27 and 36 = 9

HCF of 24 and 36 = 12

HCF of 1152 and 1664 Examples

Example 1: Find the highest number that divides 1152 and 1664 exactly. Solution:

The highest number that divides 1152 and 1664 exactly is their highest common factor, i.e. HCF of 1152 and 1664.

⇒ Factors of 1152 and 1664:

Factors of 1152 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152

Factors of 1664 = 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664

Therefore, the HCF of 1152 and 1664 is 128.

Example 2: For two numbers, HCF = 128 and LCM = 14976. If one number is 1664, find the other number.Solution:

Given: HCF (z, 1664) = 128 and LCM (z, 1664) = 14976

∵ HCF × LCM = 1664 × (z)

⇒ z = (HCF × LCM)/1664

⇒ z = (128 × 14976)/1664

⇒ z = 1152

Therefore, the other number is 1152.

Example 3: The product of two numbers is 1916928. If their HCF is 128, what is their LCM? Solution:

Given: HCF = 128 and product of numbers = 1916928

∵ LCM × HCF = product of numbers

⇒ LCM = Product/HCF = 1916928/128

Therefore, the LCM is 14976.

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FAQs on HCF of 1152 and 1664

What is the HCF of 1152 and 1664?

The . To calculate the HCF of 1152 and 1664, we need to factor each number (factors of 1152 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152; factors of 1664 = 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664) and choose the highest factor that exactly divides both 1152 and 1664, i.e., 128.

How to Find the HCF of 1152 and 1664 by Long Division Method?

To find the HCF of 1152, 1664 using long division method, 1664 is divided by 1152. The corresponding divisor (128) when remainder equals 0 is taken as HCF.

How to Find the HCF of 1152 and 1664 by Prime Factorization?

To find the HCF of 1152 and 1664, we will find the prime factorization of the given numbers, i.e. 1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3; 1664 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 13.

⇒ Since 2, 2, 2, 2, 2, 2, 2 are common terms in the prime factorization of 1152 and 1664. Hence, HCF(1152, 1664) = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128

स्रोत : www.cuemath.com

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Mohammed 1 month ago

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