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 64, 672, 886 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 64, 672, 886 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 64, 672, 886 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 64, 672, 886 is 2.
HCF(64, 672, 886) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 64, 672, 886 is 2.
Step 1: Since 672 > 64, we apply the division lemma to 672 and 64, to get
672 = 64 x 10 + 32
Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 32 and 64, to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 64 and 672 is 32
Notice that 32 = HCF(64,32) = HCF(672,64) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 886 > 32, we apply the division lemma to 886 and 32, to get
886 = 32 x 27 + 22
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 22 and 32, to get
32 = 22 x 1 + 10
Step 3: We consider the new divisor 22 and the new remainder 10, and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 32 and 886 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(886,32) .
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 64, 672, 886?
Answer: HCF of 64, 672, 886 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 64, 672, 886 using Euclid's Algorithm?
Answer: For arbitrary numbers 64, 672, 886 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.