Highest Common Factor of 741, 1029 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 741, 1029 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 1029 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 741, 1029 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 741, 1029 is 3.
HCF(741, 1029) = 3
HCF of 741, 1029 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 741, 1029 is 3.
Highest Common Factor of 741,1029 is 3
Step 1: Since 1029 > 741, we apply the division lemma to 1029 and 741, to get
1029 = 741 x 1 + 288
Step 2: Since the reminder 741 ≠ 0, we apply division lemma to 288 and 741, to get
741 = 288 x 2 + 165
Step 3: We consider the new divisor 288 and the new remainder 165, and apply the division lemma to get
288 = 165 x 1 + 123
We consider the new divisor 165 and the new remainder 123,and apply the division lemma to get
165 = 123 x 1 + 42
We consider the new divisor 123 and the new remainder 42,and apply the division lemma to get
123 = 42 x 2 + 39
We consider the new divisor 42 and the new remainder 39,and apply the division lemma to get
42 = 39 x 1 + 3
We consider the new divisor 39 and the new remainder 3,and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 741 and 1029 is 3
Notice that 3 = HCF(39,3) = HCF(42,39) = HCF(123,42) = HCF(165,123) = HCF(288,165) = HCF(741,288) = HCF(1029,741) .
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Frequently Asked Questions on HCF of 741, 1029 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 741, 1029?
Answer: HCF of 741, 1029 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 1029 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 1029 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.