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 7778, 9840 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7778, 9840 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 7778, 9840 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 7778, 9840 is 2.
HCF(7778, 9840) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7778, 9840 is 2.
Step 1: Since 9840 > 7778, we apply the division lemma to 9840 and 7778, to get
9840 = 7778 x 1 + 2062
Step 2: Since the reminder 7778 ≠ 0, we apply division lemma to 2062 and 7778, to get
7778 = 2062 x 3 + 1592
Step 3: We consider the new divisor 2062 and the new remainder 1592, and apply the division lemma to get
2062 = 1592 x 1 + 470
We consider the new divisor 1592 and the new remainder 470,and apply the division lemma to get
1592 = 470 x 3 + 182
We consider the new divisor 470 and the new remainder 182,and apply the division lemma to get
470 = 182 x 2 + 106
We consider the new divisor 182 and the new remainder 106,and apply the division lemma to get
182 = 106 x 1 + 76
We consider the new divisor 106 and the new remainder 76,and apply the division lemma to get
106 = 76 x 1 + 30
We consider the new divisor 76 and the new remainder 30,and apply the division lemma to get
76 = 30 x 2 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7778 and 9840 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(76,30) = HCF(106,76) = HCF(182,106) = HCF(470,182) = HCF(1592,470) = HCF(2062,1592) = HCF(7778,2062) = HCF(9840,7778) .
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 7778, 9840?
Answer: HCF of 7778, 9840 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7778, 9840 using Euclid's Algorithm?
Answer: For arbitrary numbers 7778, 9840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.