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 354, 907, 165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 907, 165 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 354, 907, 165 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 354, 907, 165 is 1.
HCF(354, 907, 165) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 907, 165 is 1.
Step 1: Since 907 > 354, we apply the division lemma to 907 and 354, to get
907 = 354 x 2 + 199
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 199 and 354, to get
354 = 199 x 1 + 155
Step 3: We consider the new divisor 199 and the new remainder 155, and apply the division lemma to get
199 = 155 x 1 + 44
We consider the new divisor 155 and the new remainder 44,and apply the division lemma to get
155 = 44 x 3 + 23
We consider the new divisor 44 and the new remainder 23,and apply the division lemma to get
44 = 23 x 1 + 21
We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get
23 = 21 x 1 + 2
We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get
21 = 2 x 10 + 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 354 and 907 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(44,23) = HCF(155,44) = HCF(199,155) = HCF(354,199) = HCF(907,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 165 > 1, we apply the division lemma to 165 and 1, to get
165 = 1 x 165 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 165 is 1
Notice that 1 = HCF(165,1) .
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 354, 907, 165?
Answer: HCF of 354, 907, 165 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 907, 165 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 907, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.