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If the hcf of 408 and 1032 is expressible the from 1032 p -408×5 find p?
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If the hcf of 408 and 1032 is expressible the from 1032 p -408×5 find ...
Solution :
By Euclid's division algorithm,
a = b × q + r where,
a = 1032 (Dividend)
b = 408 (Divisor)
1032 divides 408, then quotient (q) = 2 and remainder (r) = 216. So we get the values for quotient and remainder.
Substitute the values in the formula "a = b × q + r"
==> a = b × q + r
==> 1032 = 408 × 2 + 216
Multiply 408 × 2 , then we get 816. Then divide 816 by the number 2, we get 408.
==> 408 = 216 × 1+ 192
Subtract 216 (r)by the number 408 (b), we get 192.
==> 216 = 192 × 1 + 24
==> 192 = 24 × 8 + 0
==> 192 = 192
==> H.C.F = 24
==> H.C.F = 1032p - 408 × 5
==> 24 = 1032p - 2040
==> 24 + 2040 = 1032p
==> 1032p = 2064
==> p = 2064/1032
==> p = 2.
By Euclid's division algorithm,
a = b × q + r where,
a = 1032 (Dividend)
b = 408 (Divisor)
1032 divides 408, then quotient (q) = 2 and remainder (r) = 216. So we get the values for quotient and remainder.
Substitute the values in the formula "a = b × q + r"
==> a = b × q + r
==> 1032 = 408 × 2 + 216
Multiply 408 × 2 , then we get 816. Then divide 816 by the number 2, we get 408.
==> 408 = 216 × 1+ 192
Subtract 216 (r)by the number 408 (b), we get 192.
==> 216 = 192 × 1 + 24
==> 192 = 24 × 8 + 0
==> 192 = 192
==> H.C.F = 24
==> H.C.F = 1032p - 408 × 5
==> 24 = 1032p - 2040
==> 24 + 2040 = 1032p
==> 1032p = 2064
==> p = 2064/1032
==> p = 2.
Community Answer
If the hcf of 408 and 1032 is expressible the from 1032 p -408×5 find ...
Explanation:
Step 1: Find the HCF of 408 and 1032
To find the highest common factor (HCF) of 408 and 1032, we can use the Euclidean algorithm. We divide 1032 by 408 and find the remainder.
1032 ÷ 408 = 2 remainder 216
Now, we divide 408 by 216.
408 ÷ 216 = 1 remainder 192
Continuing this process, we divide 216 by 192.
216 ÷ 192 = 1 remainder 24
Next, we divide 192 by 24.
192 ÷ 24 = 8 remainder 0
Since the remainder is 0, the HCF of 408 and 1032 is 24.
Step 2: Express 24 as a combination of 1032 and 408
Now, we need to express the HCF 24 as a combination of 1032 and 408.
24 = 1032p - 408 * 5
24 = 1032p - 2040
24 + 2040 = 1032p
2064 = 1032p
p = 2064 / 1032
p = 2
Therefore, the value of p is 2.
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