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 922, 567, 42, 222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 922, 567, 42, 222 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 922, 567, 42, 222 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 922, 567, 42, 222 is 1.
HCF(922, 567, 42, 222) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 922, 567, 42, 222 is 1.
Step 1: Since 922 > 567, we apply the division lemma to 922 and 567, to get
922 = 567 x 1 + 355
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 355 and 567, to get
567 = 355 x 1 + 212
Step 3: We consider the new divisor 355 and the new remainder 212, and apply the division lemma to get
355 = 212 x 1 + 143
We consider the new divisor 212 and the new remainder 143,and apply the division lemma to get
212 = 143 x 1 + 69
We consider the new divisor 143 and the new remainder 69,and apply the division lemma to get
143 = 69 x 2 + 5
We consider the new divisor 69 and the new remainder 5,and apply the division lemma to get
69 = 5 x 13 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 922 and 567 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(69,5) = HCF(143,69) = HCF(212,143) = HCF(355,212) = HCF(567,355) = HCF(922,567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 222 > 1, we apply the division lemma to 222 and 1, to get
222 = 1 x 222 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 222 is 1
Notice that 1 = HCF(222,1) .
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 922, 567, 42, 222?
Answer: HCF of 922, 567, 42, 222 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 922, 567, 42, 222 using Euclid's Algorithm?
Answer: For arbitrary numbers 922, 567, 42, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.