Highest Common Factor of 170, 967, 993, 352 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 170, 967, 993, 352 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 967, 993, 352 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 170, 967, 993, 352 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 170, 967, 993, 352 is 1.
HCF(170, 967, 993, 352) = 1
HCF of 170, 967, 993, 352 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 967, 993, 352 is 1.
Highest Common Factor of 170,967,993,352 is 1
Step 1: Since 967 > 170, we apply the division lemma to 967 and 170, to get
967 = 170 x 5 + 117
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 117 and 170, to get
170 = 117 x 1 + 53
Step 3: We consider the new divisor 117 and the new remainder 53, and apply the division lemma to get
117 = 53 x 2 + 11
We consider the new divisor 53 and the new remainder 11,and apply the division lemma to get
53 = 11 x 4 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 170 and 967 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(53,11) = HCF(117,53) = HCF(170,117) = HCF(967,170) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 993 > 1, we apply the division lemma to 993 and 1, to get
993 = 1 x 993 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 993 is 1
Notice that 1 = HCF(993,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 352 > 1, we apply the division lemma to 352 and 1, to get
352 = 1 x 352 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 352 is 1
Notice that 1 = HCF(352,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 170, 967, 993, 352 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 170, 967, 993, 352?
Answer: HCF of 170, 967, 993, 352 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 967, 993, 352 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 967, 993, 352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.