Highest Common Factor of 222, 440, 945 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 222, 440, 945 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 440, 945 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 222, 440, 945 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 222, 440, 945 is 1.
HCF(222, 440, 945) = 1
HCF of 222, 440, 945 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 222, 440, 945 is 1.
Highest Common Factor of 222,440,945 is 1
Step 1: Since 440 > 222, we apply the division lemma to 440 and 222, to get
440 = 222 x 1 + 218
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 218 and 222, to get
222 = 218 x 1 + 4
Step 3: We consider the new divisor 218 and the new remainder 4, and apply the division lemma to get
218 = 4 x 54 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 222 and 440 is 2
Notice that 2 = HCF(4,2) = HCF(218,4) = HCF(222,218) = HCF(440,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 945 > 2, we apply the division lemma to 945 and 2, to get
945 = 2 x 472 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 945 is 1
Notice that 1 = HCF(2,1) = HCF(945,2) .
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Frequently Asked Questions on HCF of 222, 440, 945 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 222, 440, 945?
Answer: HCF of 222, 440, 945 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 440, 945 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 440, 945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.