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 7664, 4122 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7664, 4122 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 7664, 4122 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 7664, 4122 is 2.
HCF(7664, 4122) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7664, 4122 is 2.
Step 1: Since 7664 > 4122, we apply the division lemma to 7664 and 4122, to get
7664 = 4122 x 1 + 3542
Step 2: Since the reminder 4122 ≠ 0, we apply division lemma to 3542 and 4122, to get
4122 = 3542 x 1 + 580
Step 3: We consider the new divisor 3542 and the new remainder 580, and apply the division lemma to get
3542 = 580 x 6 + 62
We consider the new divisor 580 and the new remainder 62,and apply the division lemma to get
580 = 62 x 9 + 22
We consider the new divisor 62 and the new remainder 22,and apply the division lemma to get
62 = 22 x 2 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7664 and 4122 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(62,22) = HCF(580,62) = HCF(3542,580) = HCF(4122,3542) = HCF(7664,4122) .
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 7664, 4122?
Answer: HCF of 7664, 4122 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7664, 4122 using Euclid's Algorithm?
Answer: For arbitrary numbers 7664, 4122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.