Highest Common Factor of 708, 19742 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 708, 19742 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 19742 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 708, 19742 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 708, 19742 is 2.
HCF(708, 19742) = 2
HCF of 708, 19742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 19742 is 2.
Highest Common Factor of 708,19742 is 2
Step 1: Since 19742 > 708, we apply the division lemma to 19742 and 708, to get
19742 = 708 x 27 + 626
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 626 and 708, to get
708 = 626 x 1 + 82
Step 3: We consider the new divisor 626 and the new remainder 82, and apply the division lemma to get
626 = 82 x 7 + 52
We consider the new divisor 82 and the new remainder 52,and apply the division lemma to get
82 = 52 x 1 + 30
We consider the new divisor 52 and the new remainder 30,and apply the division lemma to get
52 = 30 x 1 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 708 and 19742 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(52,30) = HCF(82,52) = HCF(626,82) = HCF(708,626) = HCF(19742,708) .
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Frequently Asked Questions on HCF of 708, 19742 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 708, 19742?
Answer: HCF of 708, 19742 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 19742 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 19742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.