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 920, 563, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 920, 563, 407 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 920, 563, 407 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 920, 563, 407 is 1.
HCF(920, 563, 407) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 920, 563, 407 is 1.
Step 1: Since 920 > 563, we apply the division lemma to 920 and 563, to get
920 = 563 x 1 + 357
Step 2: Since the reminder 563 ≠ 0, we apply division lemma to 357 and 563, to get
563 = 357 x 1 + 206
Step 3: We consider the new divisor 357 and the new remainder 206, and apply the division lemma to get
357 = 206 x 1 + 151
We consider the new divisor 206 and the new remainder 151,and apply the division lemma to get
206 = 151 x 1 + 55
We consider the new divisor 151 and the new remainder 55,and apply the division lemma to get
151 = 55 x 2 + 41
We consider the new divisor 55 and the new remainder 41,and apply the division lemma to get
55 = 41 x 1 + 14
We consider the new divisor 41 and the new remainder 14,and apply the division lemma to get
41 = 14 x 2 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 920 and 563 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) = HCF(55,41) = HCF(151,55) = HCF(206,151) = HCF(357,206) = HCF(563,357) = HCF(920,563) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 1, we apply the division lemma to 407 and 1, to get
407 = 1 x 407 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 407 is 1
Notice that 1 = HCF(407,1) .
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 920, 563, 407?
Answer: HCF of 920, 563, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 920, 563, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 920, 563, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.