find the greatest number which divide 753 and 1054 leaving remainder 3 and 4 respectively
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The greatest number that will divide the numbers 753 and 1054 leaving behind the remainders 3 and 4 is 75.
- The given numbers are 753 and 1054.
- Let the greatest number which divides both the numbers be x leaving behind the remainders 3 and 4 respectively.
- As the numbers leave 3 and 4 remainders, we subtract the remainders from the numbers and find the HCF of both the numbers.
- The numbers become 750 and 1050.
- Prime factorization of the numbers is:
750 = 5 × 5 × 3 × 5 × 2
1050 = 5 × 3 × 7 × 5 × 2
HCF of both the numbers is 5 × 5 × 3 = 75.
- The greatest number that will divide the numbers 753 and 1054 leaving behind the remainders 3 and 4 is 75.
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