Highest Common Factor of 414, 672 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 414, 672 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 672 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 414, 672 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 414, 672 is 6.
HCF(414, 672) = 6
HCF of 414, 672 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 672 is 6.
Highest Common Factor of 414,672 is 6
Step 1: Since 672 > 414, we apply the division lemma to 672 and 414, to get
672 = 414 x 1 + 258
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 258 and 414, to get
414 = 258 x 1 + 156
Step 3: We consider the new divisor 258 and the new remainder 156, and apply the division lemma to get
258 = 156 x 1 + 102
We consider the new divisor 156 and the new remainder 102,and apply the division lemma to get
156 = 102 x 1 + 54
We consider the new divisor 102 and the new remainder 54,and apply the division lemma to get
102 = 54 x 1 + 48
We consider the new divisor 54 and the new remainder 48,and apply the division lemma to get
54 = 48 x 1 + 6
We consider the new divisor 48 and the new remainder 6,and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 414 and 672 is 6
Notice that 6 = HCF(48,6) = HCF(54,48) = HCF(102,54) = HCF(156,102) = HCF(258,156) = HCF(414,258) = HCF(672,414) .
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Frequently Asked Questions on HCF of 414, 672 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 414, 672?
Answer: HCF of 414, 672 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 672 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.