Question

find the greatest number that exactly divides 112 and 176​

Answer 1

Answer:

BY USING EUCLID DIVISION LEMMA

176=126*1+50

126=50*2+6

50=6*8+2

6=2*3+0

so the number is 2 that exactly divides 112 and 176

Answer 2

Answer:

The greatest number exactly divisible by 112 and 176 = 16

Explanation:

To find,

The greatest number exactly divisible by 112 and 176

Recall the concepts

The greatest number exactly divisible by 112 and 176 is the HCF of the two numbers

Solution:

Required to find the HCF of the numbers 112 and 176

The prime factorization of 112 = 2 × 2 × 2 × 2 × 7

The prime factorization of 176 = 2 × 2 × 2 × 2 × 11

The common factors of 112 and 176 are 2,2,2,2

The highest common factor of 112 and 176 = 2 × 2 × 2 × 2  = 16

∴ The greatest number exactly divisible by 112 and 176 = 16

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