Two wires 15 cm and 25 cm in length are to be cut into smaller pieces of equal length what can be the maximum length of each wire?
Answers
Answer:
- First wire = 15 cm
- Second wire = 25 cm
- Maximum equal length which can be cut from both wires = ?
When it says to find Maximum/Greatest/Longest common term, then it asks to find out Highest Common Factor (HCF)
HCF : The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor.
• According to the Question :
- We will factorise both terms first
⇒ 15 cm = 1 × 3 × 5 × cm
⇒ 25 cm = 1 × 5 × 5 × cm
⇢ HCF = 1 × 5 × cm = 5 cm
∴ Maximum equal length which can be cut from both wires is of 5 cm.
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Methods to find HCF –
- Factorization Method
- Prime Factorization Method
- Division Method
1. Factorization Method
• H.C.F. of 56 and 72.
⇢ Factor of 56 = 1, 2, 4, 6, 7, 8, 14, 28
⇢ Factor of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36
Highest Common Factor(HCF) = 8
2. Prime Factorization Method
• H.C.F. of 24, 36 and 48.
First we will find the prime factors of 24, 36 and 48.
⇢ 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. Division Method
• H.C.F. of 12 and 18.
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.
12 ) 18 ( 1
⠀⠀ 12
_______
⠀⠀ 6 ) 12 ( 2
⠀⠀ ⠀⠀ 12
⠀⠀ ________
⠀⠀ ⠀⠀ 0
H.C.F = 6
Answer:
Meaning of € =
The euro sign, €, is the currency sign used for the euro, the official currency of the Eurozone and some other countries. The design was presented to the public by the European Commission on 12 December 1996. It consists of a stylized letter E, crossed by two lines instead of one.
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Meaning of ¥ =
The yen and yuan sign, ¥, is a currency sign used for the Japanese yen and the Chinese yuan currencies when writing in Latin scripts. This monetary symbol resembles a Latin letter Y with a single or double horizontal stroke. The symbol is usually placed before the value it represents, for example: ¥50.
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Meaning of ¢ =
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Meaning of π =
The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159
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