Highest Common Factor of 360, 222 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 360, 222 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 222 is 6 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 360, 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 360, 222 is 6.
HCF(360, 222) = 6
HCF of 360, 222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 222 is 6.
Highest Common Factor of 360,222 is 6
Step 1: Since 360 > 222, we apply the division lemma to 360 and 222, to get
360 = 222 x 1 + 138
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 138 and 222, to get
222 = 138 x 1 + 84
Step 3: We consider the new divisor 138 and the new remainder 84, and apply the division lemma to get
138 = 84 x 1 + 54
We consider the new divisor 84 and the new remainder 54,and apply the division lemma to get
84 = 54 x 1 + 30
We consider the new divisor 54 and the new remainder 30,and apply the division lemma to get
54 = 30 x 1 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 360 and 222 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) = HCF(84,54) = HCF(138,84) = HCF(222,138) = HCF(360,222) .
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Frequently Asked Questions on HCF of 360, 222 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 360, 222?
Answer: HCF of 360, 222 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 222 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.