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 7758, 1340 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7758, 1340 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 7758, 1340 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 7758, 1340 is 2.
HCF(7758, 1340) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7758, 1340 is 2.
Step 1: Since 7758 > 1340, we apply the division lemma to 7758 and 1340, to get
7758 = 1340 x 5 + 1058
Step 2: Since the reminder 1340 ≠ 0, we apply division lemma to 1058 and 1340, to get
1340 = 1058 x 1 + 282
Step 3: We consider the new divisor 1058 and the new remainder 282, and apply the division lemma to get
1058 = 282 x 3 + 212
We consider the new divisor 282 and the new remainder 212,and apply the division lemma to get
282 = 212 x 1 + 70
We consider the new divisor 212 and the new remainder 70,and apply the division lemma to get
212 = 70 x 3 + 2
We consider the new divisor 70 and the new remainder 2,and apply the division lemma to get
70 = 2 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7758 and 1340 is 2
Notice that 2 = HCF(70,2) = HCF(212,70) = HCF(282,212) = HCF(1058,282) = HCF(1340,1058) = HCF(7758,1340) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 7758, 1340?
Answer: HCF of 7758, 1340 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7758, 1340 using Euclid's Algorithm?
Answer: For arbitrary numbers 7758, 1340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.