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 778, 9973 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 778, 9973 is 1 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 778, 9973 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 778, 9973 is 1.
HCF(778, 9973) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 778, 9973 is 1.
Step 1: Since 9973 > 778, we apply the division lemma to 9973 and 778, to get
9973 = 778 x 12 + 637
Step 2: Since the reminder 778 ≠ 0, we apply division lemma to 637 and 778, to get
778 = 637 x 1 + 141
Step 3: We consider the new divisor 637 and the new remainder 141, and apply the division lemma to get
637 = 141 x 4 + 73
We consider the new divisor 141 and the new remainder 73,and apply the division lemma to get
141 = 73 x 1 + 68
We consider the new divisor 73 and the new remainder 68,and apply the division lemma to get
73 = 68 x 1 + 5
We consider the new divisor 68 and the new remainder 5,and apply the division lemma to get
68 = 5 x 13 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 778 and 9973 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(68,5) = HCF(73,68) = HCF(141,73) = HCF(637,141) = HCF(778,637) = HCF(9973,778) .
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 778, 9973?
Answer: HCF of 778, 9973 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 778, 9973 using Euclid's Algorithm?
Answer: For arbitrary numbers 778, 9973 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.