Highest Common Factor of 742, 830 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 742, 830 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 830 is 2 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 742, 830 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 742, 830 is 2.
HCF(742, 830) = 2
HCF of 742, 830 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 830 is 2.
Highest Common Factor of 742,830 is 2
Step 1: Since 830 > 742, we apply the division lemma to 830 and 742, to get
830 = 742 x 1 + 88
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 88 and 742, to get
742 = 88 x 8 + 38
Step 3: We consider the new divisor 88 and the new remainder 38, and apply the division lemma to get
88 = 38 x 2 + 12
We consider the new divisor 38 and the new remainder 12,and apply the division lemma to get
38 = 12 x 3 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 742 and 830 is 2
Notice that 2 = HCF(12,2) = HCF(38,12) = HCF(88,38) = HCF(742,88) = HCF(830,742) .
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Frequently Asked Questions on HCF of 742, 830 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 742, 830?
Answer: HCF of 742, 830 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 830 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.