Find the highest common factor of (4 × 54 × 3125), (16 × 5 × 8

1.	Find the highest common factor of (4 × 54 × 3125), (16 × 5 × 8) and (32 × 27 × 11 × 49).1. 242. 403. 84. 4
Answer» Correct Answer - Option 3 : 8 Given: Numbers are (4 × 54 × 3125), (16 × 5 × 8) and (32 × 27 × 11 × 49). Concept Used: Factorization Method Calculation: 4 × 54 × 3125, ⇒ 2 × 2 × 54 × 3125 ⇒ 2 × 2 × 2 × 3 × 3 × 3 × 3125 ⇒ 2³ × 3³ × 5 × 5 × 5 × 5 × 5 ⇒ 2³ × 3³ × 5⁵ 16 × 5 × 8, ⇒ 2 × 2 × 2 × 2 × 5 × 8 ⇒ 2 × 2 × 2 × 2 × 5 × 2 × 2 × 2 ⇒ 2⁷ × 5 32 × 27 × 11 × 49 ⇒ 2 × 2 × 2 × 2 × 2 × 27 × 11 × 49 ⇒ 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 11 × 49 ⇒ 25 × 33 × 11 × 7 × 7 ⇒ 2⁵ × 3³ × 7² × 11 Now taking H.C.F. of, (23 × 33 × 55), (27 × 5) and (25 × 33 × 72 × 11) Now by taking common factors, we get ⇒ 2³ ⇒ 8 ∴ Heighest Common Factors of given numbers is 8.

Find the highest common factor of (4 × 54 × 3125), (16 × 5 × 8) and (32 × 27 × 11 × 49).1. 242. 403. 84. 4

Answer» Correct Answer - Option 3 : 8

Given:

Numbers are (4 × 54 × 3125), (16 × 5 × 8) and (32 × 27 × 11 × 49).

Concept Used:

Factorization Method

Calculation:

4 × 54 × 3125,

⇒ 2 × 2 × 54 × 3125

⇒ 2 × 2 × 2 × 3 × 3 × 3 × 3125

⇒ 2³ × 3³ × 5 × 5 × 5 × 5 × 5

⇒ 2³ × 3³ × 5⁵

16 × 5 × 8,

⇒ 2 × 2 × 2 × 2 × 5 × 8

⇒ 2 × 2 × 2 × 2 × 5 × 2 × 2 × 2

⇒ 2⁷ × 5

32 × 27 × 11 × 49

⇒ 2 × 2 × 2 × 2 × 2 × 27 × 11 × 49

⇒ 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 11 × 49

⇒ 25 × 33 × 11 × 7 × 7

⇒ 2⁵ × 3³ × 7² × 11

Now taking H.C.F. of,

(23 × 33 × 55), (27 × 5) and (25 × 33 × 72 × 11)

Now by taking common factors, we get

⇒ 2³

⇒ 8

∴ Heighest Common Factors of given numbers is 8.

Discussion

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