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 870, 964, 555 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 964, 555 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 870, 964, 555 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 870, 964, 555 is 1.
HCF(870, 964, 555) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 964, 555 is 1.
Step 1: Since 964 > 870, we apply the division lemma to 964 and 870, to get
964 = 870 x 1 + 94
Step 2: Since the reminder 870 ≠ 0, we apply division lemma to 94 and 870, to get
870 = 94 x 9 + 24
Step 3: We consider the new divisor 94 and the new remainder 24, and apply the division lemma to get
94 = 24 x 3 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 870 and 964 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(94,24) = HCF(870,94) = HCF(964,870) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 555 > 2, we apply the division lemma to 555 and 2, to get
555 = 2 x 277 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 555 is 1
Notice that 1 = HCF(2,1) = HCF(555,2) .
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 870, 964, 555?
Answer: HCF of 870, 964, 555 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 964, 555 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 964, 555 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.