Define HCF of two positive integers and find the HCF of the following pairs of numbers:(iv) 56 and 88
(v) 475 and 495
(vi) 75 and 243.
Answers
SOLUTION :
HCF (highest common factor) :
The largest positive integer that divides given two positive integers is called the Highest Common Factor of these positive integers.
(iv)Given : Two positive integers 56 and 88.
Here, 88 > 56
Let a = 88 and b = 56
88 = 56 x 1 + 32.
[By applying division lemma, a = bq + r]
Here, remainder = 32 ≠ 0, so take new dividend as 56 and new divisor as 32.
Let a = 56 and b= 32
56 = 32 x 1 + 24.
Here, remainder = 24 ≠ 0, so take new dividend as 32 and new divisor as 24.
Let a = 32 and b= 24
32 = 24 x 1+ 8.
Here, remainder = 8 ≠ 0, so take new dividend as 24 and new divisor as 8.
Let a = 24 and b= 8
24 = 8 x 3 + 0.
Here, remainder is zero and divisor is 8.
Hence ,H.C.F. of 56 and 88 is 8 .
(v) Given : Two positive integers 475 and 495.
Here, 495 > 475
Let a = 495 and b = 475
495 = 475 x 1 + 20.
[By applying division lemma, a = bq + r]
Here, remainder = 20 ≠ 0, so take new dividend as 475 and new divisor as 20.
Let a = 474 and b= 20
475 = 20 x 23 + 15.
Here, remainder = 15 ≠ 0, so take new dividend as 20 and new divisor as 15.
Let a = 20 and b= 15
20 = 15 x 1 + 5.
Here, remainder = 5 ≠ 0, so take new dividend as 15 and new divisor as 5.
Let a = 15 and b= 5
15 = 5 x 3+ 0.
Here, remainder is zero and divisor is 5.
Hence ,H.C.F. of 475 and 495 is 5
(vi) Given : Two positive integers 75 and 243.
Here, 75 > 243
Let a = 75 and b = 243
243 = 75 x 3 + 18.
[By applying division lemma, a = bq + r]
Here, remainder = 18 ≠ 0, so take new dividend as 75 and new divisor as 18.
Let a = 75 and b= 18
75 = 18 x 4 + 3.
Here, remainder = 3 ≠ 0, so take new dividend as 18 and new divisor as 3.
Let a = 18 and b= 3
18 = 3 x 6+ 0.
Here, remainder is zero and divisor is 3..
Hence ,H.C.F. of 75 and 243 is 3.
HOPE THIS ANSWER WILL HELP YOU…
Answer:
HCF OF 75,243 IS 3
Step-by-step explanation:
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