Highest Common Factor of 1737, 1074 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 1737, 1074 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1737, 1074 is 3 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 1737, 1074 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 1737, 1074 is 3.
HCF(1737, 1074) = 3
HCF of 1737, 1074 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1737, 1074 is 3.
Highest Common Factor of 1737,1074 is 3
Step 1: Since 1737 > 1074, we apply the division lemma to 1737 and 1074, to get
1737 = 1074 x 1 + 663
Step 2: Since the reminder 1074 ≠ 0, we apply division lemma to 663 and 1074, to get
1074 = 663 x 1 + 411
Step 3: We consider the new divisor 663 and the new remainder 411, and apply the division lemma to get
663 = 411 x 1 + 252
We consider the new divisor 411 and the new remainder 252,and apply the division lemma to get
411 = 252 x 1 + 159
We consider the new divisor 252 and the new remainder 159,and apply the division lemma to get
252 = 159 x 1 + 93
We consider the new divisor 159 and the new remainder 93,and apply the division lemma to get
159 = 93 x 1 + 66
We consider the new divisor 93 and the new remainder 66,and apply the division lemma to get
93 = 66 x 1 + 27
We consider the new divisor 66 and the new remainder 27,and apply the division lemma to get
66 = 27 x 2 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1737 and 1074 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(66,27) = HCF(93,66) = HCF(159,93) = HCF(252,159) = HCF(411,252) = HCF(663,411) = HCF(1074,663) = HCF(1737,1074) .
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Frequently Asked Questions on HCF of 1737, 1074 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 1737, 1074?
Answer: HCF of 1737, 1074 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1737, 1074 using Euclid's Algorithm?
Answer: For arbitrary numbers 1737, 1074 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.