Highest Common Factor of 87, 66, 88, 912 using Euclid's algorithm
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 87, 66, 88, 912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 87, 66, 88, 912 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 87, 66, 88, 912 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 87, 66, 88, 912 is 1.
HCF(87, 66, 88, 912) = 1
HCF of 87, 66, 88, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 87, 66, 88, 912 is 1.
Highest Common Factor of 87,66,88,912 is 1
Step 1: Since 87 > 66, we apply the division lemma to 87 and 66, to get
87 = 66 x 1 + 21
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 21 and 66, to get
66 = 21 x 3 + 3
Step 3: We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 87 and 66 is 3
Notice that 3 = HCF(21,3) = HCF(66,21) = HCF(87,66) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 88 > 3, we apply the division lemma to 88 and 3, to get
88 = 3 x 29 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 88 is 1
Notice that 1 = HCF(3,1) = HCF(88,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 1, we apply the division lemma to 912 and 1, to get
912 = 1 x 912 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 912 is 1
Notice that 1 = HCF(912,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 87, 66, 88, 912 using Euclid's Algorithm
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 87, 66, 88, 912?
Answer: HCF of 87, 66, 88, 912 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 87, 66, 88, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 87, 66, 88, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.