Find the largest number that divides 2053 and 967 and leaves a remainder of 5 and 7 respectively

Hint: Firstly subtract the remainders from the number so that actual numbers and can be obtained and then calculate their factors. So the common factors among both will be our required answer. Complete step-by-step answer: Given 2053 and 967 We need to find the largest number that divides 2053 and 967 leaves a remainder of 5 and 7 respectively. Calculating the actual numbers by subtracting the remainder from it as, \[ \\ \] Hence , \[64\] is our required correct answer. Note: In arithmetic, the remainder is the integer or number that is "left over" after dividing one integer or number by another to produce an integer or number quotient . In the algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. In Mathematics, factorisation is defined as the break or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc. The Remainder Theorem: When we divide a polynomial f(x) by \[x - c\] the remainder is f(c)

It is given that on dividing 2053 by the required number there is a remainder of 5 .this mean that 2053 - 5 = 2048 is exactly divisible by required number . similarly, 967?- 7 = 960 the required number is the largest number satisfying the above property . therefore ,it is?the HCF of 2048 & 960 HCF of 2048 & 960 is 64? hence required number is 64 we need remainder 5 & 7 so we subtract 5 & 7 from 2053 and 967 2053 - 5 = 2048 967 - 7 = 960 now we have to find largest number which divides them se we have to find the HCF of 2048 & 960 2048 = 960 * 2 + 128 960 = 128 * 7 + 64 128 = 64 * 2 + 0 hence 64 is the largest number that divides 2053 & 967 and leave remainder 5 & 7

Categories • • (31.9k) • (8.8k) • (764k) • (248k) • (10.0k) • (5.6k) • (36.3k) • (7.5k) • (10.7k) • (11.8k) • (11.2k) • (6.8k) • (4.9k) • (5.3k) • (2.8k) • (19.9k) • (936) • (2.9k) • (5.2k) • (664) • (121k) • (72.1k) • (3.8k) • (19.6k) • (1.4k) • (14.2k) • (12.5k) • (9.3k) • (7.7k) • (3.9k) • (6.7k) • (63.8k) • (26.6k) • (23.7k) • (14.6k) • (25.7k) • (530) • (84) • (765) • (49.1k) • (63.8k) • (1.8k) • (59.3k) • (24.5k)

It is given that on dividing 2053 by the required number there is a remainder of 5 .this mean that 2053 - 5 = 2048 is exactly divisible by required number . similarly, 967 - 7 = 960 the required number is the largest number satisfying the above property . therefore ,it is the HCF of 2048 & 960 HCF of 2048 & 960 is 64 hence required number is 64

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