Highest Common Factor of 1972, 2758 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 1972, 2758 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1972, 2758 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 1972, 2758 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 1972, 2758 is 2.
HCF(1972, 2758) = 2
HCF of 1972, 2758 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1972, 2758 is 2.
Highest Common Factor of 1972,2758 is 2
Step 1: Since 2758 > 1972, we apply the division lemma to 2758 and 1972, to get
2758 = 1972 x 1 + 786
Step 2: Since the reminder 1972 ≠ 0, we apply division lemma to 786 and 1972, to get
1972 = 786 x 2 + 400
Step 3: We consider the new divisor 786 and the new remainder 400, and apply the division lemma to get
786 = 400 x 1 + 386
We consider the new divisor 400 and the new remainder 386,and apply the division lemma to get
400 = 386 x 1 + 14
We consider the new divisor 386 and the new remainder 14,and apply the division lemma to get
386 = 14 x 27 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 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 1972 and 2758 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(386,14) = HCF(400,386) = HCF(786,400) = HCF(1972,786) = HCF(2758,1972) .
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Frequently Asked Questions on HCF of 1972, 2758 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 1972, 2758?
Answer: HCF of 1972, 2758 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1972, 2758 using Euclid's Algorithm?
Answer: For arbitrary numbers 1972, 2758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.