The hcf of two numbers is 32 and their l.c.m is 196.if one of the number s is 64, find the other number.
Answers
Step-by-step explanation:
the other number is 160.
Step-by-step explanation:
\begin{gathered}\sf Given \begin{cases} & \sf{H.C.F\:of\:two\:numbers = \bf{32}} \\ & \sf{L.C.M\:of\:two\:numbers = \bf{196}} \\ & \sf{One\:of\:the\;number\:is = \bf{64}} \end{cases}\\ \\\end{gathered}
Given
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H.C.Foftwonumbers=32
L.C.Moftwonumbers=196
Oneofthenumberis=64
To find: Other number?
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☯ Let the other number be x.
\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}
†
Asweknowthat,
\begin{gathered}\star\;{\boxed{\sf{\pink{L.C.M \times H.C.F = a \times b}}}}\\ \\\end{gathered}
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L.C.M×H.C.F=a×b
where,
a and b are two numbers.
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\begin{gathered}\dag\;{\underline{\frak{Now,\:Putting\:values\:in\:formula,}}}\\ \\\end{gathered}
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Now,Puttingvaluesinformula,
\begin{gathered}:\implies\sf 196 \times 32 = 64 \times x\\ \\\end{gathered}
:⟹196×32=64×x
\begin{gathered}:\implies\sf 6272 = 64 \times \times x\\ \\\end{gathered}
:⟹6272=64××x
\begin{gathered}:\implies\sf x = \cancel{ \dfrac{6272}{64}}\\ \\\end{gathered}
:⟹x=
64
6272
\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{x = 98}}}}}\;\bigstar\\ \\\end{gathered}
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x=98
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\therefore\:{\underline{\sf{The\:other\:number\:is\: {\textsf{\textbf{98}}}.}}}∴
Theothernumberis98.
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\begin{gathered}\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}\\ \\\end{gathered}
★Moretoknow★
HCF (Highest common factor) = The H.C.F. defines the greatest factor present in between given two or more numbers.
H.C.F. is also called the Greatest Common Factor.
LCM (Lowest common factor) = The L.C.M. defines the least number which is exactly divisible by two or more numbers.
LCM is also called the Least Common Divisor.