Find the greatest number that divides 58, 75, and 97 leaving 4, 3 and 7 respectively as remainders.
Given:
Greatest number that divides 58, 75, and 97 leaving 4, 3, and 7 respectively as remainders.
Solution:
we first subtract the remainders from the numbers:
58 - 4 = 54
75 - 3 = 72
97 - 7 = 90
Now, we find the HCF (Highest Common Factor) of 54, 72, and 90.
54 = 2 × 3³
72 = 2³ × 3²
90 = 2 × 3² × 5
The HCF of 54, 72, and 90 is 2 × 3² = 18.
Therefore, the greatest number that divides 58, 75, and 97 leaving 4, 3, and 7 respectively as remainders is 18.
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