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Find the greatest number that divides 57, 133 and 384, leaving 7, 8 and 9 respectively as remainder
Given : Numbers 57, 133 and 384.
To find: Here we have to find the greatest number that divides the numbers 57, 133 and 384 leaving reminder as 7, 8 and 9 respectively.
Solution:
If that number divide 57, 133, 384 leaving remainder 7, 8, 9 respectively, this means that number will divide 50(57 $-$ 7), 125(133 $-$ 8) and 375(384 $-$ 9) completely.
Now, we just have to find the HCF of 50, 125 and 375.
HCF of 50, 125 and 375:
- Factors of 50 = 2 $\times$ 5 $\times$ 5
- Factors of 125 = 5 $\times$ 5 $\times$ 5
- Factors of 375 = 3 $\times$ 5 $\times$ 5 $\times$ 5
Now the highest common factor is = 5 $\times$ 5 = 25.
So, the largest number that will divide 57, 133 and 384 leaving reminder as 7, 8 and 9 respectively is 25.
Updated on: 10-Oct-2022
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